Existence of minimizers for nonlevel convex supremal functionals

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

The paper is devoted to determining necessary and sufficient conditions for existence of solutions to the problem $\inf\{ {\mathop{\rm ess\: sup }}_{x\in\Omega}\, f(\nabla u(x)): u \in u_0 + W^{1,\infty}_0(\Omega)\}$, when the supremand $f$ is not necessarily level convex. These conditions are obtained through a comparison with the related level convex problem and are written in terms of a differential inclusion involving the boundary datum. Several conditions of convexity for the supremand $f$ are also investigated.Read More:http://epubs.siam.org/doi/abs/10.1137/13094390X
Original language Unknown 3341-3370 SIAM Journal on Control and Optimization 52 5 https://doi.org/10.1137/13094390X Published - 1 Jan 2014

Cite this

title = "Existence of minimizers for nonlevel convex supremal functionals",
abstract = "The paper is devoted to determining necessary and sufficient conditions for existence of solutions to the problem $\inf\{ {\mathop{\rm ess\: sup }}_{x\in\Omega}\, f(\nabla u(x)): u \in u_0 + W^{1,\infty}_0(\Omega)\}$, when the supremand $f$ is not necessarily level convex. These conditions are obtained through a comparison with the related level convex problem and are written in terms of a differential inclusion involving the boundary datum. Several conditions of convexity for the supremand $f$ are also investigated.Read More:http://epubs.siam.org/doi/abs/10.1137/13094390X",
keywords = "minimizers, supremal functionals, differential inclusions, absolute minimizers, convexity",
author = "Ribeiro, {Ana Margarida Fernandes}",
year = "2014",
month = "1",
day = "1",
doi = "10.1137/13094390X",
language = "Unknown",
volume = "52",
pages = "3341--3370",
journal = "SIAM Journal on Control and Optimization",
issn = "0363-0129",
publisher = "Siam Society for Industrial and Applied",
number = "5",

}

In: SIAM Journal on Control and Optimization, Vol. 52, No. 5, 01.01.2014, p. 3341-3370.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Existence of minimizers for nonlevel convex supremal functionals

AU - Ribeiro, Ana Margarida Fernandes

PY - 2014/1/1

Y1 - 2014/1/1

N2 - The paper is devoted to determining necessary and sufficient conditions for existence of solutions to the problem $\inf\{ {\mathop{\rm ess\: sup }}_{x\in\Omega}\, f(\nabla u(x)): u \in u_0 + W^{1,\infty}_0(\Omega)\}$, when the supremand $f$ is not necessarily level convex. These conditions are obtained through a comparison with the related level convex problem and are written in terms of a differential inclusion involving the boundary datum. Several conditions of convexity for the supremand $f$ are also investigated.Read More:http://epubs.siam.org/doi/abs/10.1137/13094390X

AB - The paper is devoted to determining necessary and sufficient conditions for existence of solutions to the problem $\inf\{ {\mathop{\rm ess\: sup }}_{x\in\Omega}\, f(\nabla u(x)): u \in u_0 + W^{1,\infty}_0(\Omega)\}$, when the supremand $f$ is not necessarily level convex. These conditions are obtained through a comparison with the related level convex problem and are written in terms of a differential inclusion involving the boundary datum. Several conditions of convexity for the supremand $f$ are also investigated.Read More:http://epubs.siam.org/doi/abs/10.1137/13094390X

KW - minimizers

KW - supremal functionals

KW - differential inclusions

KW - absolute minimizers

KW - convexity

U2 - 10.1137/13094390X

DO - 10.1137/13094390X

M3 - Article

VL - 52

SP - 3341

EP - 3370

JO - SIAM Journal on Control and Optimization

JF - SIAM Journal on Control and Optimization

SN - 0363-0129

IS - 5

ER -