Orlicz regularity of the gradient of solutions to quasilinear elliptic equations in the plane

Given a planar domain Omega, we study the Dirichlet problem {-divA(x, del v) = f in Omega, v = 0 on partial derivative Omega, where the higher-order term is a quasilinear elliptic operator, and f belongs to the Zygmund space L(log L)delta(log log log L)(beta/2) (Omega) with beta >= 0 and delta >= 1/2. We prove that the gradient of the variational solution v is an element of W-0(1,2) (Omega) belongs to the space L-2(log L)(2 delta-1)(log log log L)(beta)(Omega).


Published in:
Boundary Value Problems, 1-15
Year:
2016
Publisher:
Cham, Springer International Publishing Ag
ISSN:
1687-2770
Keywords:
Laboratories:




 Record created 2016-07-19, last modified 2018-12-03


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