A non-convex setup for multivalued differential equations driven by oblique subgradients
type: Item
instance of: scholarly article
title: A non-convex setup for multivalued differential equations driven by oblique subgradients
zbMATH Open document ID: 1307.34035
author: Aurel Răşcanu
author: Eduard Rotenstein
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2014-10-06T00:00:00Z
review text: The paper studies differential inclusions of the form \[ g(t,x(t))\in x'(t)+H(t,x(t))\partial ^{-}\varphi (x(t)), \quad t\in [0,T],\quad x(0)=x_0,\eqno (1) \] where \(H(.,.): [0,T]\times {\mathbb R}^d\to {\mathbb R}^{d\times d}\) is a matrix application such that \(x\to H(.,x)\) is Lipschitz, \(\varphi (.): {\mathbb R}^d\to (-\infty ,+\infty ]\) is a proper lower semicontinuous semiconvex function and \(x_0\in {\mathbb R}^d\). Under certain technical assumptions existence and uniqueness results for the problem considered are provided. Afterwards the global existence result obtain for problem (1) is applied in order to obtain the existence of a solution for a non-convex Skorokhod problem with generalized reflection.
reviewed by: Aurelian Cernea
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 47N10
zbMATH DE Number: 6351524
zbMATH Keywords: differential inclusions
zbMATH Keywords: oblique reflection
zbMATH Keywords: non-convex domain
zbMATH Keywords: Skorokhod problem
MaRDI profile type: Publication
full work available at URL: j.na.2014.08.020
OpenAlex ID: W1978486459
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DOI: 10.1016/J.NA.2014.08.020
description: scientific article; zbMATH DE number 6351524