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Wolff potential estimates of superminimizers of Orlicz type Dirichlet integrals. (English) Zbl 1098.35061

Summary: If \(u\) is a minimizer of \(\int_\Omega \mathbf F(| \nabla u|) dx - \int_\Omega u\,d\mu\), then the pointwise estimate \[ u(x) \leq K+C \int_0^R [\mathbf F']^{-1} \left( r^{1-n}\mu(B(x,r))\right)\,dr \] can be reached. This results is obtained for a Young function \(\mathbf F\) with the global \(\Delta_2 \& \nabla_2\) property. Links to applications to real analysis are given.

MSC:

35J20 Variational methods for second-order elliptic equations
35B45 A priori estimates in context of PDEs
35J60 Nonlinear elliptic equations
35D30 Weak solutions to PDEs
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