#2,327

Most Influential Person

American mathematician of Canadian origin

According to Wikipedia, Louis Nirenberg was a Canadian-American mathematician, considered one of the most outstanding mathematicians of the 20th century. Nearly all of his work was in the field of partial differential equations. Many of his contributions are now regarded as fundamental to the field, such as his strong maximum principle for second-order parabolic partial differential equations and the Newlander-Nirenberg theorem in complex geometry. He is regarded as a foundational figure in the field of geometric analysis, with many of his works being closely related to the study of complex analysis and differential geometry.

- Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I (1959) (3599)
- Symmetry and related properties via the maximum principle (1979) (2476)
- Positive solutions of nonlinear elliptic equations involving critical sobolev exponents (1983) (2281)
- On elliptic partial differential equations (1959) (1871)
- Partial regularity of suitable weak solutions of the navier‐stokes equations (1982) (1304)
- On functions of bounded mean oscillation (1961) (1123)
- Symmetry of positive solutions of nonlinear elliptic equations in R (1981) (1094)
- First order interpolation inequalities with weights (1984) (867)
- The Dirichlet problem for nonlinear second-order elliptic equations I (1984) (769)
- The Dirichlet problem for nonlinear second order elliptic equations, III: Functions of the eigenvalues of the Hessian (1985) (701)
- Complex Analytic Coordinates in Almost Complex Manifolds (1957) (683)
- The principal eigenvalue and maximum principle for second‐order elliptic operators in general domains (1994) (564)
- On the method of moving planes and the sliding method (1991) (564)
- Topics in Nonlinear Functional Analysis (2001) (532)
- An algebra of pseudo‐differential operators (1965) (469)
- The Weyl and Minkowski problems in differential geometry in the large (1953) (421)
- Non‐coercive boundary value problems (1965) (400)
- Remarks on finding critical points (1991) (373)
- Interior estimates for elliptic systems of partial differential equations (1955) (367)
- Partial Differential Equations Invariant under Conformal or Projective Transformations (1974) (363)
- Travelling fronts in cylinders (1992) (318)
- Characterizations of the ranges of some nonlinear operators and applications to boundary value problems (1978) (291)
- Further qualitative properties for ellip-tic equations in unbounded domains (1997) (283)
- Lectures on linear partial differential equations (1973) (272)
- The dirichlet problem for nonlinear second‐order elliptic equations. II. Complex monge‐ampère, and uniformaly elliptic, equations (1985) (264)
- H1 versus C1 local minimizers (1993) (248)
- On Spherical Image Maps Whose Jacobians Do Not Change Sign (1959) (244)
- Superlinear indefinite elliptic problems and nonlinear Liouville theorems (1994) (243)
- An extended interpolation inequality (1966) (242)
- Regularity in free boundary problems (1977) (240)
- A strong maximum principle for parabolic equations (1953) (238)
- An abstract form of the nonlinear Cauchy-Kowalewski theorem (1972) (223)
- Degree theory and BMO; part II: Compact manifolds with boundaries (1995) (220)
- Variational methods for indefinite superlinear homogeneous elliptic problems (1995) (211)
- On the analyticity of the solutions of linear elliptic systems of partial differential equations (1957) (201)
- Monotonicity for elliptic equations in unbounded Lipschitz domains (1997) (199)
- Degenerate elliptic-parabolic equations of second order (1967) (197)
- On nonlinear elliptic partial differential equations and hölder continuity (1953) (195)
- Free vibrations for a nonlinear wave equation and a theorem of P. Rabinowitz (1980) (183)
- Degree theory and BMO; part I: Compact manifolds without boundaries (1995) (177)
- Estimates for elliptic systems from composite material (2003) (173)
- The null spaces of elliptic partial differential operators in Rn (1973) (166)
- Variational and topological methods in nonlinear problems (1981) (165)
- On local solvability of linear partial differential equations part I: Necessary conditions (1970) (142)
- Solvability of a first order linear partial differential equation (1963) (139)
- Nonlinear Second-Order Elliptic Equations V. The Dirichlet Problem for Weingarten Hypersurfaces (1988) (139)
- On the Existence of Deformations of Complex Analytic Structures (1958) (138)
- Inequalities for second-order elliptic equations with applications to unbounded domains I (1996) (133)
- A remark on Ky fan's minimax principle (2008) (126)
- On stability for difference schemes; a sharp form of gårding's inequality (1966) (126)
- Some Qualitative Properties of Solutions of Semilinear Elliptic Equations in Cylindrical Domains (1990) (120)
- A pseudo-convex domain not admitting a holomorphic support function (1973) (120)
- The distance function to the boundary, Finsler geometry, and the singular set of viscosity solutions of some Hamilton-Jacobi equations† (2003) (115)
- On local solvability of linear partial differential equations—part II. Sufficient conditions† (1970) (108)
- Regularity in elliptic free boundary problems I (1978) (107)
- Lower Bounds and Uniqueness Theorems for Solutions of Differential Equations in a Hilbert Space (1967) (104)
- THE DIRICHLET PROBLEM FOR SINGULARLY PERTURBED ELLIPTIC EQUATIONS (1998) (102)
- Monotonicity, symmetry and antisymmetry of solutions of semilinear elliptic equations (1988) (101)
- A maximum principle for a class of hyperbolic equations and applications to equations of mixed elliptic-hyperbolic type† (1953) (88)
- Uniqueness in Cauchy problems for differential equations with constant leading coefficients (1957) (84)
- Intrinsic norms on a complex manifold (1996) (81)
- Remarks on Strongly Elliptic Partial Differential Equations (2015) (78)
- Properties of Solutions of Ordinary Differential Equations in Banach Space (2013) (76)
- The smoothness of the free boundary in the one phase stefan problem (1978) (72)
- Local boundary regularity of holomorphic mappings (1980) (68)
- The Dirichlet Problem for the Degenerate Monge-Ampère Equation. (1986) (61)
- Some remarks on singular solutions of nonlinear elliptic equations. I (2009) (59)
- Estimates and existence of solutions of elliptic equations (1956) (58)
- Some Remarks on Singular Solutions of Nonlinear Elliptic Equations III: Viscosity Solutions Including Parabolic Operators (2011) (57)
- Regularity of the distance function to the boundary (2005) (56)
- Forced vibrations for a nonlinear wave equation (2010) (55)
- Analyticity at the boundary of solutions of nonlinear second‐order parabolic equations (1978) (50)
- On a Theorem of P. Nowosad (1967) (50)
- A proof of the malgrange preparation theorem (1971) (49)
- ON A QUESTION OF HANS LEWY (1974) (44)
- On the chain rule for the divergence of BV-like vector fields: applications, partial results, open problems (2007) (41)
- Correction to: The dirichlet problem for nonlinear second‐order elliptic equations I. Monge‐ampere equation (1987) (40)
- Topics in nonlinear functional analysis, 1973-1974 (1974) (38)
- Degree and Sobolev spaces (1999) (38)
- Generalized Degree and Nonlinear Problems (1971) (32)
- Perspectives in nonlinear partial differential equations : in honor of Haïm Brezis (2007) (30)
- Removable singularities for nonlinear elliptic equations (1997) (27)
- Variational Methods in Nonlinear Problems (1981) (25)
- Functional analysis : New York University lectures given in 1960-61 (1961) (24)
- A celebration of John F. Nash, Jr. (1996) (22)
- VI. On a Generalization of Quasi-Conformal Mappings and its Application to Elliptic Partial Differential Equations (1955) (21)
- On a problem of Hans Lewy (1975) (20)
- Some first‐order nonlinear equations on a torus (1977) (17)
- A Convex Darboux Theorem (1997) (17)
- A geometric problem and the Hopf Lemma. I (2005) (16)
- A Complex Frobenius Theorem (2015) (15)
- A miscellany (2009) (14)
- Topics in Non-Linear Functional Analysis (2002) (13)
- Regularity of free boundaries (1976) (12)
- On the periodic solution of an ordinary differential equation of second order (1993) (11)
- A Geometric Problem and the Hopf Lemma. II (2006) (10)
- Uniqueness in the Cauchy Problem for a Degenerate Elliptic Second Order Equation (1985) (9)
- Generalization of a well-known inequality (2005) (9)
- Partial Differential Equations in the First Half of the Century (1994) (8)
- Pseudo-Differential Operators and Some Applications (1973) (8)
- Remarks on the Navier-Stokes equations (1981) (7)
- A Nonlinear Elliptic Problem Describing the Propagation of a Curved Premixed Flame (1988) (7)
- On principally linear elliptic differential equations of the second order (1993) (6)
- On the maximum principle (1992) (5)
- Scaling laws and vanishing viscosity limits in turbulence theory (2007) (4)
- A theory of degree of mapping based on infinitesimal analysis (1993) (4)
- Partial results on extending the Hopf Lemma (2009) (4)
- Abstract and Applied Analysis: Proceedings of the International Conference, Hanoi, Vietnam, 13-17 August, 2002 (2004) (3)
- Ad Honorem Charles Fefferman (2017) (3)
- Generalized implicit function theorems (2001) (3)
- Mitio Nagumo Collected Papers (1993) (3)
- On Singular Solutions of Nonlinear Elliptic and Parabolic Equations (2011) (3)
- Fully nonlinear second order elliptic equations (1988) (2)
- Regularity in an Unusual Variational Problem (2005) (2)
- Remarks on Nonlinear Problems (1980) (2)
- Lipman Bers and partial differential equations (2015) (2)
- A variational result in a domain with boundary (2000) (2)
- Degree of mapping in convex linear topological spaces (1993) (2)
- ESTIMATES FOR ELLIPTIC SYSTEMS FOR COMPOSITE MATERIAL (2004) (2)
- the short wave asymptotic behaviour of solutions of stationary problems and the asymptotic behaviour as t → ∞ of solutions of non-stationary problems (2018) (2)
- Differential equations : La Pietra 1996 : Conference on Differential Equations marking the 70th birthdays of Peter Lax and Louis Nirenberg, July 3-7, 1996, Villa La Pietra, Florence, Italy (1999) (2)
- Recent advances in partial differential equations, Venice 1996 : proceedings of a conference in honor of the 70th birthdays of Peter D. Lax and Louis Nirenberg : June 10-14, 1996, Venice, Italy (1997) (2)
- Addendum to “elliptic partial differential equations” (1953) (2)
- Pseudo-differential Operators (2011) (2)
- Propagation of singularities for linear partial differential equations and reflections at a boundary (1976) (2)
- Ventricular tachycardia caused by gold overdose. (1976) (2)
- On fully nonlinear elliptic equations of second order (1989) (1)
- SOME ASPECTS OF LINEAR AND NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS (2010) (1)
- Elliptic equations with critical nonlinear exponent (1982) (1)
- On singular perturbation of linear partial differential equations with constant coefficients, I (1993) (1)
- Elliptic partial differential equations and ordinary differential equations in Banach space (1963) (1)
- The Distance Function to the Boundary and Singular Set of Viscosity Solutions of Hamilton-Jacobi Equation (2005) (1)
- Commentary on: 42 (1985) (1)
- Degree theory beyond continuous maps (1996) (1)
- Degree of mapping of manifolds based on that of Euclidean open sets (1993) (1)
- Über die Ungleichung $$\frac{{\partial u}}{{\partial y}}>f\left({x,y,u\frac{{\partial u}}{{\partial y}}} \right)$$ (1993) (0)
- On some quasi ordinary differential equation (1993) (0)
- Topological approach: Finite dimensions (2001) (0)
- Donald C. Spencer (1912-2001), Volume 51, Number 1 (2003) (0)
- Memories of Guido Stampacchia (2005) (0)
- MATHEMATICAL STUDIES: PSEUDO-DIFFERENTIAL OPERATORS; NON-COERCIVE BOUNDARY VALUE PROBLEMS; FREDHOLM OPERATORS AND THE ESSENTIAL SPECTRUM; THE LIMITING AMPLITUDE PRINCIPAL; AND TRANSONIC FLOW. (1965) (0)
- References : of the ex- tinction limit of curved flames, Combust. Sci. and Tech. 64 (1989), 187-198. of solu- tions of semilinear elliptic equations, preprint. of solutions of semilinear (1991) (0)
- S. G. Mikhlin The spectrum of a family of operators in the theory of elasticity (2018) (0)
- A note on elliptic differental operators of the second order (1993) (0)
- Techniques in Linear and Nonlinear Partial Differential Equations (1991) (0)
- [44] (with P. R. Garabedian and H. Lewy) Axially symmetric cavitational flow (2013) (0)
- COMPLEX ANALYTIC COORDINATES IN ALMOST (2016) (0)
- CONVEXITY THEOREMS AND LOWER BOUNDS FOR SOLUTIONS OF DIFFERENTIAL EQUATIONS IN BANACH SPACE (1962) (0)
- On linear hyperbolic system of partial differential equations in the whole space (1993) (0)
- Comments on boundary value problems (1965) (0)
- Invariance of domain by completely continuous shift in function space (1993) (0)
- Further topological methods (2001) (0)
- About Olga Arsen'evna Oleinik (2004) (0)
- I.4. Minimal Surface Equation (2014) (0)
- Techniques in Linear and Nonlinear PDE's (1995) (0)
- Felix Browder (1927-2016) (2018) (0)
- Lifttng I-n Sobolev Spaces (2007) (0)
- Work of Louis Nirenberg YanYan Li (2010) (0)
- In Memoriam: Natascha Artin Brunswick, Editor Emeritus (2003) (0)
- On the Work of Louis Nirenberg Simon Donaldson (2011) (0)
- Steele Prize for Mathematical Exposition (0)
- Functional analysis, 1960-1961 (1961) (0)
- The maximum principle, moving planes et al. (2016) (0)
- Recent advances in nonlinear partial differential equations and applications : conference in honor of Peter D. Lax and Louis Nirenberg on their 80th birthdays, June 7-10, 2006, Universidad de Castilla-La Mancha at Palacio Lorenzana, Toledo, Spain (2007) (0)
- Inequalities and A Priori Estimates (2015) (0)
- A note on the theory of degree of mapping in Euclidean spaces (1993) (0)
- Louis Nirenberg Receives National Medal of Science (1997) (0)
- Ju l 2 00 5 A geometric problem and the Hopf Lemma (2008) (0)
- Topological degree in Banach space (2001) (0)
- Seminar on differential geometry in the large 1948 (1956) (0)
- Commentary on [25] (1985) (0)
- Elementary Problems: E2797-E2802 (1979) (0)
- 2 1 Se p 20 07 On the Hopf Lemma YanYan Li and Louis Nirenberg (2008) (0)
- Papers involving Variational Problems (1986) (0)
- THE MAXIMUM PRINCIPLE AND RELATED TOPICS (1996) (0)
- Quantities and real numbers (1993) (0)
- Monotone operators and the min-max theorem (2001) (0)
- On Some Variational Methods (1983) (0)
- Re-topologization of functional space in order that a set of operators will be continuous (1993) (0)
- Reduction of Operators of First Order to Canonical Forms (1973) (0)
- Part I. An a priori estimate (1982) (0)
- LECTURE SERIES IN DIFFERENTIAL EQUATIONS. SESSION 4. DIFFERENTIAL OPERATORS (1966) (0)

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Louis Nirenberg is affiliated with the following schools:

- New York University
- McGill University
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