Boundary Value Problems for Mixed Type Equations and Applications

TL;DR

This paper develops a general method for formulating well-posed boundary value problems for mixed elliptic-hyperbolic equations, extending previous techniques, and applies it to nonlinear equations in differential geometry.

Contribution

It introduces a new general approach for boundary value problems for mixed type equations and applies it to nonlinear equations in geometry.

Findings

Extended techniques for well-posed boundary problems.

Application to nonlinear mixed type equations in geometry.

Framework applicable to a broad class of mixed equations.

Abstract

In this paper we outline a general method for finding well-posed boundary value problems for linear equations of mixed elliptic and hyperbolic type, which extends previous techniques of Berezanskii, Didenko, and Friedrichs. This method is then used to study a particular class of fully nonlinear mixed type equations which arise in applications to differential geometry.