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.
Regularity for multi-phase variational problems / De Filippis, C.; Oh, J.. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 267:3(2019), pp. 1631-1670. [10.1016/j.jde.2019.02.015]
Regularity for multi-phase variational problems
De Filippis C.;
2019-01-01
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.File in questo prodotto:
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