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Higher differentiability for solutions of stationary p ‐Stokes systems
Author(s) -
Giannetti Flavia,
Passarelli di Napoli Antonia,
Scheven Christoph
Publication year - 2020
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201800519
Subject(s) - mathematics , differentiable function , dimension (graph theory) , type (biology) , function (biology) , term (time) , mathematical analysis , stationary point , pure mathematics , physics , ecology , quantum mechanics , evolutionary biology , biology
We consider weak solutions( u , π ) : Ω → R n × R to stationary p ‐Stokes systems of the type− div a ( x , E u ) + ∇ π + [ D u ] u = f ,div u = 0in Ω ⊂ R n , where the function a ( x , ξ ) satisfies p ‐growth conditions in ξ and depends Hölder continuously on x . By E u we denote the symmetric part of the gradient D u and we write [ D u ] u for the convective term. In this setting, we establish results on the fractional higher differentiability of both the symmetric part of the gradient E u and of the pressure π. As an application, we deduce dimension estimates for the singular set of the gradient D u , thereby improving known results on partial C 1 , α ‐regularity for solutions to stationary p ‐Stokes systems.