Dirichlet problem for degenerate elliptic equations

The Dirichlet Problem for Nonuniformly Elliptic Equations

and repeated indices indicate summation from 1 to n. The functions a'(x, u, p), a(x, u, p) are defined in QX£ n + 1 . If furthermore for any ikf>0, the ratio of the maximum to minimum eigenvalues of [a(Xy u, p)] is bounded in ÛX( — M, M)XE, Qu is called uniformly elliptic. A solution of the Dirichlet problem Qu = Q, u—<f)(x) on <50 is a C(n)P\C(O) function u(x) satisfying Qu = 0 in £2 and agree...

Existence Results for a Dirichlet Quasilinear Elliptic Problem

In this paper, existence results of positive classical solutions for a class of second-order differential equations with the nonlinearity dependent on the derivative are established. The approach is based on variational methods.

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

On the Dirichlet boundary problem for quasi–degenerate elliptic linear equations

Motivated by the structure of the Dynamics Programming Equations relative to Controlled Diffusions we study the Dirichlet value boundary problem governed by quasi–degenerate elliptic partial differential equations of second order. Interior properties of the solution involved to the Maximum Principle are also considered in the paper. 2000 Mathematics Subject Classification: 35B50, 35B37, 49L25

On the Dirichlet Problem for Non-totally Degenerate Fully Nonlinear Elliptic Equations

We prove some comparison principles for viscosity solutions of fully nonlinear degenerate elliptic equations that satisfy conditions of partial non-degeneracy instead of the usual uniform ellipticity or strict monotonicity. These results are applied to the well-posedness of the Dirichlet problem under suitable conditions at the characteristic points of the boundary. The examples motivating the ...