Solvability of monotone systems of fully nonlinear elliptic PDE's

Solvability of monotone systems of fully nonlinear elliptic PDE's

Solvability of uniformly elliptic fully nonlinear PDE

We get existence, uniqueness and non-uniqueness of viscosity solutions of uniformly elliptic fully nonlinear equations of Hamilton-Jacobi-BellmanIsaacs type, with unbounded ingredients and quadratic growth in the gradient, without hypotheses of convexity or properness. Some of our results are new even for equations in divergence form.

UNIQUENESS OF VISCOSITY SOLUTIONS FOR MONOTONE SYSTEMS OF FULLY NONLINEAR PDES UNDER DIRICHLET CONDITIONt

is a given function, where L2 is a bounded open set of R” and S” is the set of symmetric matrices of order n. Several authors have studied some systems of PDEs via viscosity solution methods; e.g. [l-5]. Recently, Ishii and Koike [6] have pointed out that these systems have a monotone structure and have obtained uniqueness results under the assumption of monotonicity on F. Moreover, Ishii [7] h...

On Schwarz Methods for Monotone Elliptic PDEs

The Schwarz Alternating Method was devised by H. A. Schwarz more than one hundred years ago to solve linear boundary value problems. It has garnered interest recently because of its potential as an efficient algorithm for parallel computers. See [Lio88], and [Lio89], the recent reviews [CM94], [LT94], and [XZ98], and the books [SBG96] and [QV99]. The literature for nonlinear problems is rather ...

On the Unique Solvability of Some Nonlinear Stochastic Pdes

The Cauchy problem for 1-dimensional nonlinear stochastic partial differential equations is studied. The uniqueness and existence of solutions in Hp(T )-space are proved. 1991 Mathematics Subject Classification. 60H15, 35R60.