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Nonlinear gradient estimates for elliptic equations in quasiconvex domains
Journal article   Peer reviewed

Nonlinear gradient estimates for elliptic equations in quasiconvex domains

Sun-Sig Byun, Hun Kwon, Hyoungsuk So and Lihe Wang
Calculus of variations and partial differential equations, Vol.54(2), pp.1425-1453
10/2015
DOI: 10.1007/s00526-015-0830-5

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Abstract

We study a general model of nonvariational elliptic equations of \(p\)-Laplacian type in quasiconvex domains, which are locally approximated by convex domains. We prove that both the gradient and the associated nonhomogeneous term belong to the same \(L^q\) space for every \(q \in [p, \infty )\). As far as the domain is concerned, our regularity assumption on the boundary is weaker than any other one reported in this direction. In addition, we extend our result in Lebesgue spaces to Orlicz spaces.
Mathematics Analysis Calculus of Variations and Optimal Control; Optimization Systems Theory, Control Theoretical, Mathematical and Computational Physics

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