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Regularity results for a class of obstacle problems

Authors:

Michela Eleuteri

Institution:

(1) WIAS—Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117 Berlin, Germany

Abstract:

We prove some optimal regularity results for minimizers of the integral functional ∫ f(x, u, Du) dx belonging to the class K ≔ {u ∈ W ^1,p(Ω): u ⩾ ψ, where ψ is a fixed function, under standard growth conditions of p-type, i.e.

$L^{ - 1} \left| z \right|^p \leqslant f(x,s,z) \leqslant L(1 + \left| z \right|^p ).$

. This research has been supported by INdAM. On leave from: Dipartimento di Matematica, Universitá di Trento, via Sommarive 14, 38050 Povo (Trento), Italy, e-mail: eleuteri@science.unitn.it.

Keywords:

regularity results local minimizers integral functionals obstacle problems standard growth conditions

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