- Department of Mathematics
- University of California
- Berkeley, CA, 94720-3840

Math 123: Ordinary Differential Equations

Envelopes and nonconvex Hamilton--Jacobi equations

Monotonicity formulas for variational problems

Everywhere differentiability of infinity harmonic functions

Adjoint methods for the infinity Laplacian PDE

Adjoint and compensated compactness methods for Hamilton--Jacobi PDE

A ``lakes and rivers'' interpretation for the singular limit of a nonlinear diffusion PDE

Further PDE methods for weak KAM theory

C^{1, \alpha} regularity for infinity harmonic functions in two dimensions

The 1-Laplacian, the infinity Laplacian and differential games

The infinity Laplacian, Aronsson's equation and their generalizations

Diffeomorphisms and nonlinear heat flows SIAM Journal Mathematical Analysis 37 (2005)

Various properties of solutions to the infinity Laplacian equation Communications in Partial Differential Equations 30 (2005)

Irreversibility and hysteresis for a forward-backwards diffusion equation Math Models and Methods in Applied Sciences 14 (2004)

A survey of entropy methods for partial differential equations Bulletin AMS 41 (2004)

A survey of partial differential equations methods in weak KAM theory Comm in Pure and Applied Math 57 (2004)

Towards a quantum analog of weak KAM theory Communications Math Physics 244 (2004)

Integral estimates for transport densities Bulletin LMS 36 (2004)

Three singular variational problems RIMS Conference 1323 (2003)

On some singular limits of homogeneous semigroups J Evolution Equations 3 (2003)

Some new PDE methods for weak KAM theory Calculus of Variations and PDE 17 (2003)

Linear programming interpretations of Mather's variational principle Control, Optimization and Cal of Variations 8 (2002)

An asymptotic model for compression molding Indiana U Math Journal 50 (2002)

Effective Hamiltonians and averaging for Hamiltonian dynamics I Archive Rational Mechanics and Analysis 157 (2001)

Effective Hamiltonians and averaging for Hamiltonian dynamics II Archive Rational Mechanics and Analysis 161 (2002)

Effective Hamiltonians and quantum states Seminar Ecole Polytechnique 2000-2001

Optimal Lipschitz extensions and the infinity Laplacian Calculus of Variations and PDE 13 (2001)

Transparencies for lectures
on ''Recent developments in weak convergence methods for
nonlinear PDE''

(given as a short course at SIAM meeting, July, 2006).
References.

Lecture notes: Version 0.2 for an undergraduate course "An Introduction to Mathematical Optimal Control Theory".

Lecture notes for a graduate course "Entropy and Partial Differential Equations".

Survey of applications of PDE methods to Monge-Kantorovich mass transfer problems (an earlier version of which appeared in Current Developments in Mathematics, 1997).

Errata for the first edition of "Partial Differential Equations" by L. C. Evans, (American Math Society, first printing 1998)

Errata for the book "Measure Theory and Fine Properties of Functions" (CRC Press, 1992, first printing), by L. C. Evans and R. F. Gariepy.

Errata for the article ``Variational Methods", in ``The Princeton Companion to Mathematics'', 2008.