Existence of minimizers for nonlevel convex supremal functionals

Ana Margarida Fernandes Ribeiro

doi:10.1137/13094390X

Existence of minimizers for nonlevel convex supremal functionals

Ana Margarida Fernandes Ribeiro

DM - Departamento de Matemática

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

17 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
Pages (from-to)	3341-3370
Journal	SIAM Journal on Control and Optimization
Volume	52
Issue number	5
DOIs	https://doi.org/10.1137/13094390X
Publication status	Published - 1 Jan 2014

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10.1137/13094390X

Cite this

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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",

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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

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DO - 10.1137/13094390X

M3 - Article

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SP - 3341

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JO - SIAM Journal on Control and Optimization

JF - SIAM Journal on Control and Optimization

IS - 5

ER -