Michael G. Crandall | Academic Influence

Michael G. Crandall's AcademicInfluence.com Rankings

Michael G. Crandall

Mathematics

#1051

World Rank

#1803

Historical Rank

#456

USA Rank

Measure Theory

#618

World Rank

#851

Historical Rank

#251

USA Rank

mathematics Degrees

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Mathematics

Michael G. Crandall's Degrees

PhD Mathematics University of California, Berkeley

Why Is Michael G. Crandall Influential?

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According to Wikipedia, Michael Grain Crandall is an American mathematician, specializing in differential equations. Mathematical career In 1962 Crandall earned a baccalaureate in engineering physics from University of California, Berkeley, changed to mathematics, earning a master's in 1964 and a PhD in 1965 under Heinz Cordes at Berkeley, with a thesis that solved a problem in celestial mechanics posed by Carl Ludwig Siegel; the thesis title is Two families of plane solutions of the four body problem. In 1965 he was an instructor at Berkeley, in 1966 an assistant professor at Stanford University and from 1969 at the University of California, Los Angeles , where he was a professor from 1973 to 1976. From 1974 to 1984 he was a professor at the Mathematics Research Center at the University of Wisconsin–Madison, from 1984 to 1990 as Hille-Professor of Mathematics. From 1988 until his retirement he was a professor at the University of California, Santa Barbara. Crandall was several times a visiting professor at the University of Paris, where he received an honorary doctorate in 1999. His legacy of contributions contains all but not limited to: Banach solutions in Euclidean spaces, Fourier transforms of planar variables, PDE concepts and iterations for sequence analysis, semigroup transform solutions, differential harmonic study of divergent hyperbole, physical transformations of finite Jacobian entities, unique harmonic populations in convergent contexts, application of abstract existence principles on non-linear contexts, normalized vector sequencing in multi-dimensional parallax geometries, and the mathematical equivalence study of topographical dissimilar nodes using traditional non-linear surfacing theories to produce distinct solutions in the realm of differential multi-variable applications.

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Michael G. Crandall's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

User’s guide to viscosity solutions of second order partial differential equations (1992) (4725)
Bifurcation from simple eigenvalues (1971) (1762)
Viscosity solutions of Hamilton-Jacobi equations (1983) (1356)
Some Properties of Viscosity Solutions of Hamilton-Jacobi Equations. (1984) (1242)
GENERATION OF SEMI-GROUPS OF NONLINEAR TRANSFORMATIONS ON GENERAL BANACH SPACES, (1971) (871)
Bifurcation, perturbation of simple eigenvalues, itand linearized stability (1973) (762)
Two approximations of solutions of Hamilton-Jacobi equations (1984) (674)
Monotone difference approximations for scalar conservation laws (1979) (445)
Some continuation and variational methods for positive solutions of nonlinear elliptic eigenvalue problems (1975) (440)
Stabilization of solutions of a degenerate nonlinear diffusion problem (1982) (378)
On a dirichlet problem with a singular nonlinearity (1977) (361)
A TOUR OF THE THEORY OF ABSOLUTELY MINIMIZING FUNCTIONS (2004) (351)
Nonlinear evolution equations in Banach spaces (1972) (289)
Optimal Lipschitz extensions and the infinity laplacian (2001) (255)
Some relations between nonexpansive and order preserving mappings (1980) (254)
Semi-groups of nonlinear contractions and dissipative sets☆ (1969) (236)
Perturbations of nonlinear maximal monotone sets in banach space (1970) (231)
Solutions of the Porous Medium Equation in R(N) under Optimal Conditions on Initial Values. (1982) (187)
Hamilton-Jacobi equations in infinite dimensions I. Uniqueness of viscosity solutions (1985) (183)
The semigroup approach to first order quasilinear equations in several space variables (1972) (179)
Viscosity solutions: A primer (1997) (170)
The Hopf Bifurcation Theorem in infinite dimensions (1977) (168)
The method of fractional steps for conservation laws (1980) (153)
Regularizing Effects of Homogeneous Evolution Equations (1980) (152)
On viscosity solutions of fully nonlinear equations with measurable ingredients (1996) (151)
On Some Existence Theorems for Semi-Linear Elliptic Equations. (1977) (145)
Lp- Theory for fully nonlinear uniformly parabolic equations (2000) (145)
Hamilton-Jacobi equations in infinite dimensions. II. Existence of viscosity solutions (1986) (142)
Hamilton-Jacobi equations in infinite dimensions, III (1986) (125)
A semilinear equation in $L^1 (\mathbb {R}^N)$ (1975) (120)
The maximum principle for semicontinuous functions (1990) (119)
A Semilinear Equation in L1(rn) (2007) (118)
Viscosity solutions of Hamilton-Jacobi equations in infinite dimensions. IV: Hamiltonians with unbounded linear terms (1990) (114)
An Introduction to Evolution Governed by Accretive Operators (1976) (113)
Existence results for boundary problems for uniformly elliptic and parabolic fully nonlinear equations (1999) (113)
Hamilton-Jacobi Equations in Infinite Dimensions (2003) (100)
Uniqueness of viscosity solutions of Hamilton-Jacobi equations revisited (1987) (91)
Nonlinear Semigroups and Evolution Governed by Accretive Operators. (1984) (90)
A Visit with the ∞-Laplace Equation (2008) (87)
Viscosity solutions and applications : lectures given at the 2nd session of the Centro internazionale matematico estivo (C.I.M.E.) held in Montecatini Terme, Italy, June 12-20, 1995 (1997) (86)
On existence and uniqueness of solutions of Hamilton-Jacobi equations (1986) (86)
Convergent difference schemes for nonlinear parabolic equations and mean curvature motion (1996) (85)
Some Problems in Nonlinear Analysis (1990) (84)
An abstract functional differential equation and a related nonlinear Volterra equation (1977) (79)
Viscosity solutions of Hamilton-Jacobi equations in infinite dimensions. V. Unbounded linear terms and B-continuous solutions (1991) (77)
SomeL1 existence and dependence results for semilinear elliptic equations under nonlinear boundary conditions (1988) (77)
An abstract nonlinear Volterra integrodifferential equation (1978) (75)
On the relation of the operator ∂/∂s+∂/∂τ to evolution governed by accretive operators (1975) (74)
Regularizing effects for ut + Aϑ(u) = 0 in L1 (1982) (72)
Remarks on the Existence and Uniqueness of Unbounded Viscosity Solutions of Hamilton-Jacobi Equations. (1987) (65)
A generalization of Peano’s existence theorem and flow invariance (1972) (62)
A generalized domain for semigroup generators (1973) (60)
Maximal solutions and universal bounds for some partial differential equations of evolution (1989) (57)
Uniqueness of ∞-Harmonic Functions and the Eikonal Equation (2007) (50)
Viscosity Solutions of Fully Nonlinear Equations (1994) (46)
Calculus of Variations and Nonlinear Partial Differential Equations (2007) (46)
An Efficient Derivation of the Aronsson Equation (2003) (45)
Differential equations on convex sets (1970) (40)
A semilinear elliptic equation in L[1] (IR[n]) (1975) (36)
A remark on infinity harmonic functions. (2001) (35)
On the range of accretive operators (1977) (35)
Viscosity Solutions of Hamilton-Jacobi Equations in Infinite Dimensions. VII. The HJB Equation Is Not Always Satisfied (1994) (34)
Directions in partial differential equations (1987) (33)
Semigroups of Nonlinear Transformations in Banach Spaces (1971) (33)
REMARKS ON NONLINEAR UNIFORMLY PARABOLIC EQUATIONS (1998) (33)
Hamilton-Jacobi Equations in Infinite Dimensions. Part 1. Uniqueness of Viscosity Solutions, (1984) (31)
Viscosity solutions of Hamilton-Jacobi equations at the boundary (1985) (30)
Mathematical Theory of Bifurcation (1980) (30)
Contributions To Nonlinear Functional Analysis (1971) (30)
Convergence of difference approximations of quasilinear evolution equations (1986) (29)
Another way to say harmonic (2002) (29)
ON THE EQUIVALENCE OF VARIOUS WEAK NOTIONS OF SOLUTIONSOF ELLIPTIC PDES WITH MEASURABLE INGREDIENTS (1996) (29)
Distance Functions and Almost Global Solutions of Eikonal Equations (2010) (28)
Uniqueness of Solutions of the Initial-Value Problem for u sub t - delta phi(u) = 0. (1978) (28)
Semidifferentials, quadratic forms and fully nonlinear elliptic equations of second order (1989) (26)
Convexity Criteria and Uniqueness of Absolutely Minimizing Functions (2010) (26)
Derivation of the Aronsson equation for C1 Hamiltonians (2008) (26)
Another way to say caloric (2003) (26)
The Hopf Bifurcation Theorem. (1976) (26)
On the extension problem for dissipative operators (1968) (25)
Norm preserving extensions of linear transformations on Hilbert spaces. (1969) (25)
On accretive sets in Banach spaces (1970) (25)
A theorem and a counterexample in the theory of semigroups of nonlinear transformations (1971) (23)
Semigroups, theory and applications (1986) (20)
TO VISCOSITY SOLUTIONS OF SECOND ORDER PARTIAL DIFFERENTIAL EQUATIONS (1992) (20)
Remarks on generators of analytic semigroups (1979) (20)
Developments in the Theory of Nonlinear First-Order Partial Differential Equations (1984) (17)
Regularizing effects for _{}=Δ() (1982) (13)
Regularizing Effects for u t = ??(u) (1982) (13)
THE PRINCIPLE OF EXCHANGE OF STABILITY (1977) (12)
Nonlinear Evolution Equations. (1982) (11)
On nonlinear equations of evolution (1989) (11)
Quadratic growth of solutions of fully nonlinear second order equations in $\mathbb{R}^n$ (1990) (10)
A singular semilinear equation in (1977) (10)
Existence and uniqueness for viscosity solutions of degenerate quasilinear elliptic equations in rn (1989) (10)
Two Families of Periodic Solutions of the Plane Four-Body Problem (1967) (9)
Hamilton-Jacobi Equations in Infinite Dimensions. Part 3. (1986) (9)
An Approximation of Integrable Functions by Step Functions with an Application. (1979) (8)
A Note on Generalized Maximum Principles for Elliptic and Parabolic PDE (2019) (6)
On nonuniqueness of viscosity solutions (1992) (6)
A Singular Semilinear Equation in L 1 (R) (1977) (5)
Viscosity Solutions of Hamilton-Jacobi Equations in Banach Spaces (1985) (5)
A remark on semilinear perturbations of abstract parabolic equations (1985) (4)
Multiple solutions of a nonlinear integral equation (1970) (4)
A Semilinear Elliptic Equation in (L sup 1)(R sup N). (1975) (4)
Quasinonlinear Evolution Equations. (1982) (2)
THE PROBLEM OF TWO STICKS (2010) (2)
Viscosity solutions of partial differential equations (1991) (2)
ON APPROXIMATE SOLUTIONS TO ONE CLASS OF NON-LINEAR DIRICHLET ELLIPTIC BOUNDARY VALUE PROBLEMS (2)
On the Relation of the Operator Partial derivative with respect to s + Partial derivative with respect to tau to Evolution Governed by Accretive Operators. (1975) (1)
Relations between geometric convexity, doubling measures and property Γ (2014) (1)
Boundary Value Problems for Symmetric Positive Differential Operators of Odd Order (1968) (1)
The Continuous Dependence on psi of Solutions of u sub t - (delta)psi(u) = O. (1979) (1)
Regularizing Effects for u sub t = Delta (psi (u)). (1981) (1)
Nonlinear evolution equations : proceedings of a symposium (1978) (1)
On Regularization of an Optimal Control Problem for Ill-Posed Nonlinear Elliptic Equations (2020) (0)
Existence and Uniqueness Viscosity Solutions of Degenerate Quasilinear Elliptic Equations in R(N). Revision (1988) (0)
The maximum principle, semicontinuity and nonlinear PDE's (1990) (0)
SOME RELATIONS BETWEEN NONEXPANSTVE AND ORDER PRESERVING MAPPINGS 1 (2010) (0)
Review: Viorel Barbu, Nonlinear semigroups and differential equations in Banach spaces (1978) (0)
Regularizing Effects for u sub t + A(psi(u))=0 in L1 Vector Space. (1981) (0)
Introduction. Dedicated to Philippe Bénilan (2003) (0)
Almost Global Solutions of the Eikonal Equation (2004) (0)
A Singular Semilinear Equation in (L superscript 1)(R). (1975) (0)
Preprint Version: May 30, 2009 THE PROBLEM OF TWO STICKS (2009) (0)

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