Besov regularity for solutions of elliptic equations with variable exponents

Raffaella Giova

Mathematische Nachrichten, 2020, vol. 293, issue 8, 1459-1480

Abstract: We establish the higher fractional differentiability of the solutions of a problem in divergence form of the type divA(x,Du)=div|F|p(x)−22FinΩ,u=0on∂Ω.The main features consist in assuming that the partial map ξ→A(x,ξ) has p(x)‐growth, the datum F is Besov regular and both the partial map x→A(x,ξ) and the function x→p(x) are Orlicz–Besov regular.

Date: 2020
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https://doi.org/10.1002/mana.201900185

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