The Dirichlet problem for a class of nonlinear degenerate parabolic equations

Solvability of Nonlinear Dirichlet Problem for a Class of Degenerate Elliptic Equations

The Cauchy-dirichlet Problem for a General Class of Parabolic Equations

We prove regularity results such as interior Lipschitz regularity and boundary continuity for the Cauchy-Dirichlet problem associated to a class of parabolic equations inspired by the evolutionary p-Laplacian, but extending it at a wide scale. We employ a regularization technique of viscosity-type that we find interesting in itself.

Numerical solution of the Dirichlet problem for nonlinear parabolic equations by a probabilistic approach

A number of new layer methods for solving the Dirichlet problem for semilinear parabolic equations are constructed by using probabilistic representations of their solutions. The methods exploit the ideas of weak sense numerical integration of stochastic differential equations in a bounded domain. Despite their probabilistic nature these methods are nevertheless deterministic. Some convergence t...

A finite volume scheme for nonlinear degenerate parabolic equations

We propose a second order finite volume scheme for nonlinear degenerate parabolic equations. For some of these models (porous media equation, drift-diffusion system for semiconductors, ...) it has been proved that the transient solution converges to a steady-state when time goes to infinity. The present scheme preserves steady-states and provides a satisfying long-time behavior. Moreover, it re...

The Dirichlet Problem for Degenerate Complex Monge-ampere Equations

The Dirichlet problem for a Monge-Ampère equation corresponding to a nonnegative, possible degenerate cohomology class on a Kähler manifold with boundary is studied. C1,α estimates away from a divisor are obtained, by combining techniques of Blocki, Tsuji, Yau, and pluripotential theory. In particular, C1,α geodesic rays in the space of Kähler potentials are constructed for each test configurat...