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Summer 2000 Non-Linear Balayage and applications
Murali Rao, Jan Sokolowski
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Illinois J. Math. 44(2): 310-328 (Summer 2000). DOI: 10.1215/ijm/1255984843

Abstract

A theory of capacities has been extentively studied for Besov spaces [1]. However not much seems to have been done regarding non-linear potentials. We develop some of this here as consequences of the form of certain metric projections.

The non-linear potential theory is used to derive the form of tangent cones for a class of convex sets in Besov spaces. Tangent cones for obstacle problem arise when studying differentiability of metric projection. Characterising the tangent cones is the first step in these considerations. This has been done in some of the Sobolev spaces using Hilbert space methods. In this article we describe tangent cones for obstacle problems precisely, using non-linear potential theoretic ideas, for all Besov spaces $B^{p,q}_{\alpha}$, $1 \lt p \lt \infty$, $1 \lt q \lt \infty$, $\alpha \gt 0$.

Citation

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Murali Rao. Jan Sokolowski. "Non-Linear Balayage and applications." Illinois J. Math. 44 (2) 310 - 328, Summer 2000. https://doi.org/10.1215/ijm/1255984843

Information

Published: Summer 2000
First available in Project Euclid: 19 October 2009

zbMATH: 0980.31006
MathSciNet: MR1775324
Digital Object Identifier: 10.1215/ijm/1255984843

Subjects:
Primary: 31C45
Secondary: 31C15 , 46E35 , 49J50

Rights: Copyright © 2000 University of Illinois at Urbana-Champaign

Vol.44 • No. 2 • Summer 2000
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