Regularity for multi-phase variational problems

Cristiana De Filippis; Jehan Oh

doi:10.1016/j.jde.2019.02.015

Regularity for multi-phase variational problems

Cristiana De Filippis, Jehan Oh

University of Oxford

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

69 Scopus citations

Abstract

We prove C ^1,ν -regularity for local minimizers of the multi-phase energy: w↦∫Ω|Dw| ^p +a(x)|Dw| ^q +b(x)|Dw| ^s dx, under sharp assumptions relating the couples (p,q) and (p,s) to the Hölder exponents of the modulating coefficients a(⋅) and b(⋅), respectively.

Original language	English
Pages (from-to)	1631-1670
Number of pages	40
Journal	Journal of Differential Equations
Volume	267
Issue number	3
DOIs	https://doi.org/10.1016/j.jde.2019.02.015
State	Published - 15 Jul 2019

Keywords

Minimizer
Multi-phase
Non-uniformly elliptic problems
Regularity

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10.1016/j.jde.2019.02.015

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abstract = " We prove C 1,ν -regularity for local minimizers of the multi-phase energy: w↦∫Ω|Dw| p +a(x)|Dw| q +b(x)|Dw| s dx, under sharp assumptions relating the couples (p,q) and (p,s) to the H{\"o}lder exponents of the modulating coefficients a(⋅) and b(⋅), respectively.",

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N2 - We prove C 1,ν -regularity for local minimizers of the multi-phase energy: w↦∫Ω|Dw| p +a(x)|Dw| q +b(x)|Dw| s dx, under sharp assumptions relating the couples (p,q) and (p,s) to the Hölder exponents of the modulating coefficients a(⋅) and b(⋅), respectively.

AB - We prove C 1,ν -regularity for local minimizers of the multi-phase energy: w↦∫Ω|Dw| p +a(x)|Dw| q +b(x)|Dw| s dx, under sharp assumptions relating the couples (p,q) and (p,s) to the Hölder exponents of the modulating coefficients a(⋅) and b(⋅), respectively.

KW - Minimizer

KW - Multi-phase

KW - Non-uniformly elliptic problems

KW - Regularity

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M3 - Article

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EP - 1670

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 3

ER -

Regularity for multi-phase variational problems

Abstract

Keywords

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