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Besov regularity for solutions of elliptic equations with variable exponents

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  • Raffaella Giova

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.

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  • Raffaella Giova, 2020. "Besov regularity for solutions of elliptic equations with variable exponents," Mathematische Nachrichten, Wiley Blackwell, vol. 293(8), pages 1459-1480, August.
    • Handle: RePEc:bla:mathna:v:293:y:2020:i:8:p:1459-1480
    DOI: 10.1002/mana.201900185
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    References listed on IDEAS

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    1. Alexandre Almeida & Lars Diening & Peter Hästö, 2018. "Homogeneous variable exponent Besov and Triebel–Lizorkin spaces," Mathematische Nachrichten, Wiley Blackwell, vol. 291(8-9), pages 1177-1190, June.
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    Cited by:

    1. Fengping Yao, 2023. "Besov estimates for weak solutions of a class of quasilinear parabolic equations with general growth," Mathematische Nachrichten, Wiley Blackwell, vol. 296(7), pages 3034-3055, July.

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