Elliptic gradient constraint problem

Hi Jun Choe; Phoui Souksomvang

doi:10.1080/03605302.2016.1237962

Elliptic gradient constraint problem

Hi Jun Choe, Phoui Souksomvang

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

We study the existence and regularity of gradient constraint problem. It arises in elastoplasticity and finance. First, we consider linear double obstacle problem which comes from viscosity solution to Hamilton–Jacobi equation and find the solution has C^1,α regularity by estimating Campanato-type integral oscillation. Then, by perturbation method and fixed point theorem in C^1,α space, we prove the existence of C^1,α solution.

Original language	English
Pages (from-to)	1918-1933
Number of pages	16
Journal	Communications in Partial Differential Equations
Volume	41
Issue number	12
DOIs	https://doi.org/10.1080/03605302.2016.1237962
Publication status	Published - 2016 Dec 1

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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abstract = "We study the existence and regularity of gradient constraint problem. It arises in elastoplasticity and finance. First, we consider linear double obstacle problem which comes from viscosity solution to Hamilton–Jacobi equation and find the solution has C1,α regularity by estimating Campanato-type integral oscillation. Then, by perturbation method and fixed point theorem in C1,α space, we prove the existence of C1,α solution.",

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AB - We study the existence and regularity of gradient constraint problem. It arises in elastoplasticity and finance. First, we consider linear double obstacle problem which comes from viscosity solution to Hamilton–Jacobi equation and find the solution has C1,α regularity by estimating Campanato-type integral oscillation. Then, by perturbation method and fixed point theorem in C1,α space, we prove the existence of C1,α solution.

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