#1,548

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) (3909)
- Symmetry and related properties via the maximum principle (1979) (2683)
- Positive solutions of nonlinear elliptic equations involving critical sobolev exponents (1983) (2522)
- On elliptic partial differential equations (1959) (2387)
- Partial regularity of suitable weak solutions of the navier‐stokes equations (1982) (1499)
- Symmetry of positive solutions of nonlinear elliptic equations in R (1981) (1207)
- On functions of bounded mean oscillation (1961) (1026)
- First order interpolation inequalities with weights (1984) (989)
- The Dirichlet problem for nonlinear second-order elliptic equations I (1984) (887)
- The Dirichlet problem for nonlinear second order elliptic equations, III: Functions of the eigenvalues of the Hessian (1985) (810)
- Complex Analytic Coordinates in Almost Complex Manifolds (1957) (727)
- On the method of moving planes and the sliding method (1991) (626)
- The principal eigenvalue and maximum principle for second‐order elliptic operators in general domains (1994) (617)
- An algebra of pseudo‐differential operators (1965) (500)
- The Weyl and Minkowski problems in differential geometry in the large (1953) (469)
- Topics in Nonlinear Functional Analysis (2001) (446)
- Non‐coercive boundary value problems (1965) (434)
- Interior estimates for elliptic systems of partial differential equations (1955) (400)
- Partial Differential Equations Invariant under Conformal or Projective Transformations (1974) (399)
- Remarks on finding critical points (1991) (395)
- Travelling fronts in cylinders (1992) (326)
- Further qualitative properties for ellip-tic equations in unbounded domains (1997) (310)
- The dirichlet problem for nonlinear second‐order elliptic equations. II. Complex monge‐ampère, and uniformaly elliptic, equations (1985) (305)
- Characterizations of the ranges of some nonlinear operators and applications to boundary value problems (1978) (302)
- An extended interpolation inequality (1966) (298)
- H1 versus C1 local minimizers (1993) (280)
- Regularity in free boundary problems (1977) (279)
- On Spherical Image Maps Whose Jacobians Do Not Change Sign (1959) (273)
- Superlinear indefinite elliptic problems and nonlinear Liouville theorems (1994) (260)
- A strong maximum principle for parabolic equations (1953) (250)
- An abstract form of the nonlinear Cauchy-Kowalewski theorem (1972) (242)
- Degree theory and BMO; part I: Compact manifolds without boundaries (1995) (240)
- Lectures on linear partial differential equations (1973) (236)
- Variational methods for indefinite superlinear homogeneous elliptic problems (1995) (232)
- Monotonicity for elliptic equations in unbounded Lipschitz domains (1997) (224)
- Degree theory and BMO; part II: Compact manifolds with boundaries (1995) (223)
- On the analyticity of the solutions of linear elliptic systems of partial differential equations (1957) (217)
- On nonlinear elliptic partial differential equations and hölder continuity (1953) (209)
- Degenerate elliptic-parabolic equations of second order (1967) (207)
- Free vibrations for a nonlinear wave equation and a theorem of P. Rabinowitz (1980) (195)
- Variational and topological methods in nonlinear problems (1981) (172)
- The null spaces of elliptic partial differential operators in Rn (1973) (170)
- Estimates for elliptic systems from composite material (2003) (161)
- Nonlinear Second-Order Elliptic Equations V. The Dirichlet Problem for Weingarten Hypersurfaces (1988) (156)
- On local solvability of linear partial differential equations part I: Necessary conditions (1970) (156)
- A remark on Ky fan's minimax principle (2008) (155)
- On the Existence of Deformations of Complex Analytic Structures (1958) (150)
- Inequalities for second-order elliptic equations with applications to unbounded domains I (1996) (149)
- Solvability of a first order linear partial differential equation (1963) (144)
- On local solvability of linear partial differential equations—part II. Sufficient conditions† (1970) (142)
- On stability for difference schemes; a sharp form of gårding's inequality (1966) (134)
- Some Qualitative Properties of Solutions of Semilinear Elliptic Equations in Cylindrical Domains (1990) (132)
- Regularity in elliptic free boundary problems I (1978) (128)
- A pseudo-convex domain not admitting a holomorphic support function (1973) (125)
- The distance function to the boundary, Finsler geometry, and the singular set of viscosity solutions of some Hamilton‐Jacobi equations (2003) (122)
- Monotonicity, symmetry and antisymmetry of solutions of semilinear elliptic equations (1988) (112)
- Lower Bounds and Uniqueness Theorems for Solutions of Differential Equations in a Hilbert Space (1967) (112)
- THE DIRICHLET PROBLEM FOR SINGULARLY PERTURBED ELLIPTIC EQUATIONS (1998) (111)
- Intrinsic norms on a complex manifold (1996) (93)
- Remarks on Strongly Elliptic Partial Differential Equations (2015) (91)
- A maximum principle for a class of hyperbolic equations and applications to equations of mixed elliptic-hyperbolic type† (1953) (89)
- Uniqueness in Cauchy problems for differential equations with constant leading coefficients (1957) (89)
- Properties of Solutions of Ordinary Differential Equations in Banach Space (2013) (84)
- The smoothness of the free boundary in the one phase stefan problem (1978) (79)
- Local boundary regularity of holomorphic mappings (1980) (75)
- Some remarks on singular solutions of nonlinear elliptic equations. I (2009) (72)
- The Dirichlet Problem for the Degenerate Monge-Ampère Equation. (1986) (70)
- Regularity of the distance function to the boundary (2005) (68)
- Some Remarks on Singular Solutions of Nonlinear Elliptic Equations III: Viscosity Solutions Including Parabolic Operators (2011) (67)
- Estimates and existence of solutions of elliptic equations (1956) (64)
- Forced vibrations for a nonlinear wave equation (2010) (63)
- Analyticity at the boundary of solutions of nonlinear second‐order parabolic equations (1978) (53)
- A proof of the malgrange preparation theorem (1971) (51)
- On a Theorem of P. Nowosad (1967) (50)
- ON A QUESTION OF HANS LEWY (1974) (48)
- On the chain rule for the divergence of BV-like vector fields: applications, partial results, open problems (2007) (48)
- Degree and Sobolev spaces (1999) (40)
- Topics in nonlinear functional analysis, 1973-1974 (1974) (37)
- Perspectives in nonlinear partial differential equations : in honor of Haïm Brezis (2007) (33)
- Generalized Degree and Nonlinear Problems (1971) (31)
- Correction to: The dirichlet problem for nonlinear second‐order elliptic equations I. Monge‐ampere equation (1987) (27)
- Removable singularities for nonlinear elliptic equations (1997) (27)
- A celebration of John F. Nash, Jr. (1996) (25)
- Variational Methods in Nonlinear Problems (1992) (25)
- On a problem of Hans Lewy (1975) (24)
- Functional analysis : New York University lectures given in 1960-61 (1961) (23)
- VI. On a Generalization of Quasi-Conformal Mappings and its Application to Elliptic Partial Differential Equations (1955) (21)
- A Convex Darboux Theorem (2002) (18)
- A Complex Frobenius Theorem (2015) (17)
- Topics in Non-Linear Functional Analysis (2002) (17)
- A Geometric Problem and the Hopf Lemma. II (2005) (17)
- Some first‐order nonlinear equations on a torus (1977) (17)
- On Singular Solutions of Nonlinear Elliptic and Parabolic Equations (2011) (17)
- A miscellany (2009) (16)
- Regularity of free boundaries (1976) (12)
- Generalization of a well-known inequality (2005) (11)
- On the periodic solution of an ordinary differential equation of second order (1993) (11)
- Uniqueness in the Cauchy Problem for a Degenerate Elliptic Second Order Equation (1985) (10)
- Ju l 2 00 5 A geometric problem and the Hopf Lemma (2008) (9)
- Pseudo-Differential Operators and Some Applications (1973) (8)
- Partial Differential Equations in the First Half of the Century (1994) (8)
- On the Hopf Lemma (2007) (8)
- A Nonlinear Elliptic Problem Describing the Propagation of a Curved Premixed Flame (1988) (7)
- A theory of degree of mapping based on infinitesimal analysis (1993) (7)
- On principally linear elliptic differential equations of the second order (1993) (5)
- Remarks on the Navier-Stokes equations (1981) (5)
- Scaling laws and vanishing viscosity limits in turbulence theory (2007) (5)
- Partial results on extending the Hopf Lemma (2009) (5)
- Generalized implicit function theorems (2001) (4)
- ESTIMATES FOR ELLIPTIC SYSTEMS FOR COMPOSITE MATERIAL (2004) (4)
- On the maximum principle (1992) (4)
- the short wave asymptotic behaviour of solutions of stationary problems and the asymptotic behaviour as t → ∞ of solutions of non-stationary problems (2018) (3)
- Mitio Nagumo Collected Papers (1993) (3)
- Abstract and Applied Analysis: Proceedings of the International Conference, Hanoi, Vietnam, 13-17 August, 2002 (2004) (3)
- Ad Honorem Charles Fefferman (2017) (3)
- Pseudo-differential Operators (2011) (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)
- Propagation of singularities for linear partial differential equations and reflections at a boundary (1976) (2)
- Ventricular tachycardia caused by gold overdose. (1976) (2)
- Remarks on Nonlinear Problems (1980) (2)
- Addendum to “elliptic partial differential equations” (1953) (2)
- Regularity in an Unusual Variational Problem (2005) (2)
- A variational result in a domain with boundary (2000) (2)
- Fully nonlinear second order elliptic equations (1988) (2)
- Lipman Bers and partial differential equations (2015) (2)
- Elliptic equations with critical nonlinear exponent (1982) (1)
- Degree of mapping of manifolds based on that of Euclidean open sets (1993) (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 in convex linear topological spaces (1993) (1)
- Elliptic partial differential equations and ordinary differential equations in Banach space (1963) (1)
- On fully nonlinear elliptic equations of second order (1989) (1)
- On singular perturbation of linear partial differential equations with constant coefficients, I (1993) (1)
- SOME ASPECTS OF LINEAR AND NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS (2010) (1)
- THE MAXIMUM PRINCIPLE AND RELATED TOPICS (1996) (0)
- Techniques in Linear and Nonlinear Partial Differential Equations (1991) (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)
- Lifttng I-n Sobolev Spaces (2007) (0)
- Memories of Guido Stampacchia (2005) (0)
- I.4. Minimal Surface Equation (2014) (0)
- Steele Prize for Mathematical Exposition (0)
- On linear hyperbolic system of partial differential equations in the whole space (1993) (0)
- Quantities and real numbers (1993) (0)
- Seminar on differential geometry in the large 1948 (1956) (0)
- On Some Variational Methods (1983) (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)
- Work of Louis Nirenberg YanYan Li (2010) (0)
- Über die Ungleichung $$\frac{{\partial u}}{{\partial y}}>f\left({x,y,u\frac{{\partial u}}{{\partial y}}} \right)$$ (1993) (0)
- A note on the theory of degree of mapping in Euclidean spaces (1993) (0)
- Part I. An a priori estimate (1982) (0)
- Infinitely Many Periodic Solutions for the Equation: u-u+_lul (0)
- Topological approach: Finite dimensions (2001) (0)
- Papers involving Variational Problems (1986) (0)
- Donald C. Spencer (1912-2001), Volume 51, Number 1 (2003) (0)
- Inequalities and A Priori Estimates (2015) (0)
- S. G. Mikhlin The spectrum of a family of operators in the theory of elasticity (2018) (0)
- CONVEXITY THEOREMS AND LOWER BOUNDS FOR SOLUTIONS OF DIFFERENTIAL EQUATIONS IN BANACH SPACE (1962) (0)
- Felix Browder (1927-2016) (2018) (0)
- Functional analysis, 1960-1961 (1961) (0)
- Comments on boundary value problems (1965) (0)
- [44] (with P. R. Garabedian and H. Lewy) Axially symmetric cavitational flow (2013) (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)
- About Olga Arsen'evna Oleinik (2004) (0)
- In Memoriam: Natascha Artin Brunswick, Editor Emeritus (2003) (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)
- A note on elliptic differental operators of the second order (1993) (0)
- Louis Nirenberg Receives National Medal of Science (1997) (0)
- Monotone operators and the min-max theorem (2001) (0)
- On some quasi ordinary differential equation (1993) (0)
- Techniques in Linear and Nonlinear PDE's (1995) (0)
- LECTURE SERIES IN DIFFERENTIAL EQUATIONS. SESSION 4. DIFFERENTIAL OPERATORS (1966) (0)
- The maximum principle, moving planes et al. (2016) (0)
- Commentary on [25] (1985) (0)
- COMPLEX ANALYTIC COORDINATES IN ALMOST (2016) (0)
- 2 1 Se p 20 07 On the Hopf Lemma YanYan Li and Louis Nirenberg (2008) (0)
- Invariance of domain by completely continuous shift in function space (1993) (0)
- On the Work of Louis Nirenberg Simon Donaldson (2011) (0)
- Further topological methods (2001) (0)
- Elementary Problems: E2797-E2802 (1979) (0)
- Topological degree in Banach space (2001) (0)

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