Semicontinuous viscosity solutions to mixed boundary value problems with degenerate convex Hamiltonians
type: Item
instance of: scholarly article
title: Semicontinuous viscosity solutions to mixed boundary value problems with degenerate convex Hamiltonians
zbMATH Open document ID: 1006.35024
DOI: 10.1016/S0362-546X(01)00137-7
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2003-03-04T00:00:00Z
review text: This paper is devoted to the study of a boundary value problem of the form \[ \begin{cases} H(x,Du,u_k)+ \lambda u=0\quad &\text{in }\Omega\times (0, \infty),\\ H(x,Du,u_k)+ \lambda u=0\quad &\text{or }u=g\text{ on }\partial\Omega \times (0,\infty),\\ H(x,Du,u_k) +\lambda u\geq 0\quad &\text{on }\Omega\times \{0\},\end{cases} \tag{1} \] where \(\Omega\) is an open subset of \(\mathbb{R}^n\), and \(g\) is a bounded lower semicontinuous function. Here the authors prove the uniqueness of the solution to (1) in the viscosity sense, and show its existence by giving a representation formula in terms of the value function of an exit time control problem.
Mathematics Subject Classification ID: 35F30
Mathematics Subject Classification ID: 49L25
zbMATH DE Number: 1751605
zbMATH Keywords: representation formula
zbMATH Keywords: exit time control problem
author: M. Motta
author: C. Sartori
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
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full work available at URL: s0362-546x(01)00137-7
OpenAlex ID: W1967066503
description: scientific article; zbMATH DE number 1751605