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Regularity results for a class of obstacle problems with $p,q-$growth conditions | | Michele Caselli
; Michela Eleuteri
; Antonia Passarelli di Napoli
; | | Date: |
19 Jul 2019 | | Abstract: | In this paper we prove the local boundedness as well as the local Lipschitz
continuity for solutions to a class of obstacle problems of the type
$$minleft{int_Omega {F(x, Dz)}: zin mathcal{K}_{psi}(Omega)
ight}.$$
Here $mathcal{K}_{psi}(Omega)$ is set of admissible functions $z in
W^{1,p}(Omega)$ such that $z ge psi$ a.e. in $Omega$, $psi$ being the
obstacle and $Omega$ being an open bounded set of $mathbb{R}^n$, $n ge 2$.
The main novelty here is that we are assuming $ F(x, Dz)$ satisfying
$(p,q)$-growth conditions {and less restrictive assumptions on the obstacle
with respect to the existing regularity results}. | | Source: | arXiv, 1907.8527 | | Services: | Forum | Review | PDF | Favorites | |
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