# Louis Nirenberg

American mathematician of Canadian origin

## Louis Nirenberg's AcademicInfluence.com Rankings

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Mathematics

## Why Is Louis Nirenberg Influential?

(Suggest an Edit or Addition)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.

## Louis Nirenberg's Published Works

### Published Works

- Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I (1959) (3984)
- Symmetry and related properties via the maximum principle (1979) (2727)
- Positive solutions of nonlinear elliptic equations involving critical sobolev exponents (1983) (2611)
- On elliptic partial differential equations (1959) (2499)
- Partial regularity of suitable weak solutions of the navier‐stokes equations (1982) (1532)
- Symmetry of positive solutions of nonlinear elliptic equations in R (1981) (1236)
- On functions of bounded mean oscillation (1961) (1034)
- First order interpolation inequalities with weights (1984) (1029)
- The Dirichlet problem for nonlinear second-order elliptic equations I (1984) (918)
- The Dirichlet problem for nonlinear second order elliptic equations, III: Functions of the eigenvalues of the Hessian (1985) (847)
- Complex Analytic Coordinates in Almost Complex Manifolds (1957) (736)
- On the method of moving planes and the sliding method (1991) (646)
- The principal eigenvalue and maximum principle for second‐order elliptic operators in general domains (1994) (628)
- An algebra of pseudo‐differential operators (1965) (523)
- The Weyl and Minkowski problems in differential geometry in the large (1953) (482)
- Topics in Nonlinear Functional Analysis (2001) (443)
- Non‐coercive boundary value problems (1965) (443)
- Partial Differential Equations Invariant under Conformal or Projective Transformations (1974) (411)
- Interior estimates for elliptic systems of partial differential equations (1955) (407)
- Remarks on finding critical points (1991) (401)
- Travelling fronts in cylinders (1992) (330)
- The dirichlet problem for nonlinear second‐order elliptic equations. II. Complex monge‐ampère, and uniformaly elliptic, equations (1985) (318)
- Further qualitative properties for ellip-tic equations in unbounded domains (1997) (317)
- An extended interpolation inequality (1966) (307)
- Characterizations of the ranges of some nonlinear operators and applications to boundary value problems (1978) (306)
- H1 versus C1 local minimizers (1993) (285)
- Regularity in free boundary problems (1977) (285)
- On Spherical Image Maps Whose Jacobians Do Not Change Sign (1959) (277)
- Superlinear indefinite elliptic problems and nonlinear Liouville theorems (1994) (263)
- A strong maximum principle for parabolic equations (1953) (255)
- Degree theory and BMO; part I: Compact manifolds without boundaries (1995) (249)
- An abstract form of the nonlinear Cauchy-Kowalewski theorem (1972) (248)
- Lectures on linear partial differential equations (1973) (236)
- Monotonicity for elliptic equations in unbounded Lipschitz domains (1997) (234)
- Variational methods for indefinite superlinear homogeneous elliptic problems (1995) (234)
- Degree theory and BMO; part II: Compact manifolds with boundaries (1995) (226)
- On the analyticity of the solutions of linear elliptic systems of partial differential equations (1957) (221)
- On nonlinear elliptic partial differential equations and hölder continuity (1953) (214)
- Degenerate elliptic-parabolic equations of second order (1967) (212)
- Free vibrations for a nonlinear wave equation and a theorem of P. Rabinowitz (1980) (200)
- Variational and topological methods in nonlinear problems (1981) (174)
- The null spaces of elliptic partial differential operators in Rn (1973) (172)
- A remark on Ky fan's minimax principle (2008) (167)
- Estimates for elliptic systems from composite material (2003) (166)
- Nonlinear Second-Order Elliptic Equations V. The Dirichlet Problem for Weingarten Hypersurfaces (1988) (163)
- On local solvability of linear partial differential equations part I: Necessary conditions (1970) (159)
- Inequalities for second-order elliptic equations with applications to unbounded domains I (1996) (152)
- On the Existence of Deformations of Complex Analytic Structures (1958) (150)
- Solvability of a first order linear partial differential equation (1963) (148)
- On local solvability of linear partial differential equations—part II. Sufficient conditions† (1970) (143)
- On stability for difference schemes; a sharp form of gårding's inequality (1966) (136)
- A pseudo-convex domain not admitting a holomorphic support function (1973) (128)
- The distance function to the boundary, Finsler geometry, and the singular set of viscosity solutions of some Hamilton‐Jacobi equations (2003) (125)
- Monotonicity, symmetry and antisymmetry of solutions of semilinear elliptic equations (1988) (116)
- Lower Bounds and Uniqueness Theorems for Solutions of Differential Equations in a Hilbert Space (1967) (115)
- THE DIRICHLET PROBLEM FOR SINGULARLY PERTURBED ELLIPTIC EQUATIONS (1998) (111)
- Intrinsic norms on a complex manifold (1996) (98)
- Remarks on Strongly Elliptic Partial Differential Equations (2015) (96)
- A maximum principle for a class of hyperbolic equations and applications to equations of mixed elliptic-hyperbolic type† (1953) (94)
- Uniqueness in Cauchy problems for differential equations with constant leading coefficients (1957) (90)
- Properties of Solutions of Ordinary Differential Equations in Banach Space (2013) (89)
- The smoothness of the free boundary in the one phase stefan problem (1978) (81)
- Local boundary regularity of holomorphic mappings (1980) (77)
- Some remarks on singular solutions of nonlinear elliptic equations. I (2009) (73)
- Regularity of the distance function to the boundary (2005) (72)
- The Dirichlet Problem for the Degenerate Monge-Ampère Equation. (1986) (72)
- Some Remarks on Singular Solutions of Nonlinear Elliptic Equations III: Viscosity Solutions Including Parabolic Operators (2011) (71)
- Forced vibrations for a nonlinear wave equation (2010) (65)
- Estimates and existence of solutions of elliptic equations (1956) (64)
- Analyticity at the boundary of solutions of nonlinear second‐order parabolic equations (1978) (53)
- A proof of the malgrange preparation theorem (1971) (52)
- On a Theorem of P. Nowosad (1967) (51)
- On the chain rule for the divergence of BV-like vector fields: applications, partial results, open problems (2007) (49)
- ON A QUESTION OF HANS LEWY (1974) (48)
- Degree and Sobolev spaces (1999) (39)
- 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)
- A celebration of John F. Nash, Jr. (1996) (28)
- Correction to: The dirichlet problem for nonlinear second‐order elliptic equations I. Monge‐ampere equation (1987) (28)
- Removable singularities for nonlinear elliptic equations (1997) (27)
- Variational Methods in Nonlinear Problems (1992) (25)
- On a problem of Hans Lewy (1975) (25)
- 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) (19)
- On Singular Solutions of Nonlinear Elliptic and Parabolic Equations (2011) (18)
- A Complex Frobenius Theorem (2015) (18)
- Some first‐order nonlinear equations on a torus (1977) (17)
- A Geometric Problem and the Hopf Lemma. II (2005) (17)
- Topics in Non-Linear Functional Analysis (2002) (17)
- A miscellany (2009) (16)
- On the periodic solution of an ordinary differential equation of second order (1993) (12)
- Regularity of free boundaries (1976) (12)
- Generalization of a well-known inequality (2005) (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)
- On the Hopf Lemma (2007) (9)
- Partial Differential Equations in the First Half of the Century (1994) (8)
- A theory of degree of mapping based on infinitesimal analysis (1993) (7)
- Pseudo-Differential Operators and Some Applications (1973) (7)
- Scaling laws and vanishing viscosity limits in turbulence theory (2007) (5)
- Partial results on extending the Hopf Lemma (2009) (5)
- Remarks on the Navier-Stokes equations (1981) (5)
- Generalized implicit function theorems (2001) (4)
- On principally linear elliptic differential equations of the second order (1993) (4)
- ESTIMATES FOR ELLIPTIC SYSTEMS FOR COMPOSITE MATERIAL (2004) (4)
- On the maximum principle (1992) (4)
- Mitio Nagumo Collected Papers (1993) (3)
- the short wave asymptotic behaviour of solutions of stationary problems and the asymptotic behaviour as t → ∞ of solutions of non-stationary problems (2018) (3)
- Ad Honorem Charles Fefferman (2017) (3)
- Abstract and Applied Analysis: Proceedings of the International Conference, Hanoi, Vietnam, 13-17 August, 2002 (2004) (3)
- Pseudo-differential Operators (2011) (3)
- Addendum to “elliptic partial differential equations” (1953) (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)
- Fully nonlinear second order elliptic equations (1988) (2)
- Propagation of singularities for linear partial differential equations and reflections at a boundary (1976) (2)
- Lipman Bers and partial differential equations (2015) (2)
- Remarks on Nonlinear Problems (1980) (2)
- Regularity in an Unusual Variational Problem (2005) (2)
- A variational result in a domain with boundary (2000) (2)
- Ventricular tachycardia caused by gold overdose. (1976) (2)
- Elliptic equations with critical nonlinear exponent (1982) (1)
- Degree of mapping of manifolds based on that of Euclidean open sets (1993) (1)
- On fully nonlinear elliptic equations of second order (1989) (1)
- The Distance Function to the Boundary and Singular Set of Viscosity Solutions of Hamilton-Jacobi Equation (2005) (1)
- SOME ASPECTS OF LINEAR AND NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS (2010) (1)
- Degree of mapping in convex linear topological spaces (1993) (1)
- Elliptic partial differential equations and ordinary differential equations in Banach space (1963) (1)
- Degree theory beyond continuous maps (1996) (1)
- Commentary on: 42 (1985) (1)
- On singular perturbation of linear partial differential equations with constant coefficients, I (1993) (1)
- Topological degree in Banach space (2001) (0)
- Elementary Problems: E2797-E2802 (1979) (0)
- Über die Ungleichung $$\frac{{\partial u}}{{\partial y}}>f\left({x,y,u\frac{{\partial u}}{{\partial y}}} \right)$$ (1993) (0)
- Infinitely Many Periodic Solutions for the Equation: u-u+_lul (0)
- THE MAXIMUM PRINCIPLE AND RELATED TOPICS (1996) (0)
- Papers involving Variational Problems (1986) (0)
- Further topological methods (2001) (0)
- [44] (with P. R. Garabedian and H. Lewy) Axially symmetric cavitational flow (2013) (0)
- Monotone operators and the min-max theorem (2001) (0)
- On linear hyperbolic system of partial differential equations in the whole space (1993) (0)
- About Olga Arsen'evna Oleinik (2004) (0)
- Inequalities and A Priori Estimates (2015) (0)
- Re-topologization of functional space in order that a set of operators will be continuous (1993) (0)
- Felix Browder (1927-2016) (2018) (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)
- Louis Nirenberg Receives National Medal of Science (1997) (0)
- Part I. An a priori estimate (1982) (0)
- On Some Variational Methods (1983) (0)
- In Memoriam: Natascha Artin Brunswick, Editor Emeritus (2003) (0)
- On the Work of Louis Nirenberg Simon Donaldson (2011) (0)
- Donald C. Spencer (1912-2001), Volume 51, Number 1 (2003) (0)
- Topological approach: Finite dimensions (2001) (0)
- Quantities and real numbers (1993) (0)
- Invariance of domain by completely continuous shift in function space (1993) (0)
- Seminar on differential geometry in the large 1948 (1956) (0)
- Techniques in Linear and Nonlinear Partial Differential Equations (1991) (0)
- On some quasi ordinary differential equation (1993) (0)
- LECTURE SERIES IN DIFFERENTIAL EQUATIONS. SESSION 4. DIFFERENTIAL OPERATORS (1966) (0)
- The maximum principle, moving planes et al. (2016) (0)
- Reduction of Operators of First Order to Canonical Forms (1973) (0)
- Lifttng I-n Sobolev Spaces (2007) (0)
- Steele Prize for Mathematical Exposition (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)
- Memories of Guido Stampacchia (2005) (0)
- 2 1 Se p 20 07 On the Hopf Lemma YanYan Li and Louis Nirenberg (2008) (0)
- I.4. Minimal Surface Equation (2014) (0)
- A note on elliptic differental operators of the second order (1993) (0)
- COMPLEX ANALYTIC COORDINATES IN ALMOST (2016) (0)
- Work of Louis Nirenberg YanYan Li (2010) (0)
- S. G. Mikhlin The spectrum of a family of operators in the theory of elasticity (2018) (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 the theory of degree of mapping in Euclidean spaces (1993) (0)
- Comments on boundary value problems (1965) (0)
- Techniques in Linear and Nonlinear PDE's (1995) (0)
- Commentary on [25] (1985) (0)
- Functional analysis, 1960-1961 (1961) (0)
- CONVEXITY THEOREMS AND LOWER BOUNDS FOR SOLUTIONS OF DIFFERENTIAL EQUATIONS IN BANACH SPACE (1962) (0)

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