A Holder continuity result for a class of obstacle problems under non standard growth conditions

作者：Eleuteri Michela; Habermann Jens^*

来源：Mathematische Nachrichten, 2011, 284(11-12): 1404-1434.

DOI：10.1002/mana.200810147

• Regularity
• Holder continuity
• local minimizers
• obstacle problems

We prove C(0,alpha) regularity for local minimizers u of functionals with p(x)-growth of the type
F(w, Omega) := integral(Omega) f(x, w(x), Dw(x)) dx,
in the class K := {w is an element of W(1,p(.))(Omega; R) : w >= psi}, where the exponent function p : Omega -> (1, infinity) is assumed to be continuous with a modulus of continuity satisfying
lim(p -> 0) sup omega(rho) log (1/rho) < +infinity,
and 1 < gamma(1) <= p(x) <= gamma(2) < +infinity. Moreover, psi is an element of W(loc)(1, 1) is a given obstacle function, whose gradient D psi belongs to a Morrey space L(loc)(q,lambda) (Omega) with n - gamma(1) < lambda < n and q > gamma(2). We do not assume any quantitative continuity of the integrand function f.

• 出版日期2011-8