Calderón–Zygmund type estimates for a class of obstacle problems with p(x) growth

By Michela Eleuteri, J. Habermann. 2010

48 citations recorded by the source corpus.

For local minimizers u∈Wloc1,p(⋅)(Ω) of quasiconvex integral functionals of the type F[u]:=∫Ωf(x,Du(x))dx with p(x) growth in the class K:={u∈Wloc1,p(⋅)(Ω):u⩾ψ}, where ψ∈Wloc1,p(⋅)(Ω) is a given obstacle function, we show estimates of Calderon–Zygmund type, i.e. |Dψ|p(⋅)∈Llocq⇒|Du|p(⋅)∈Llocq, for any q>1, provided that the modulus of continuity ω of the exponent function p satisfies the condition ω(ρ)log1ρ→0as ρ→0.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/f31c96057a3dd417f312ef34cfc53043b59655ad

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Partial regularity of $p(x)$-harmonic maps (2011, background): “For the scalar valued case (n=1), see [17, 4, 8, 9, 10, 11] and the references therein.”
Higher differentiability for solutions to a class of obstacle problems (2018, background): “Since then, many regularity results have been obtained in different situations: for instance we quote [16] in the setting of Morrey and Campanato spaces, [8,17,19,37] in the setting of nonstandard growth conditions (see also [9,18,38] for Calderón–Zygmund case).”
Calderón–Zygmund theory for nonlinear elliptic problems with irregular obstacles (2012, methodology): “In [14] Eleuteri and Habermann obtained estimates of Calderón–Zygmund type for one-sided obstacle problems considering local minimizers of quasi-convex integral functionals with p(x) growth.”