MATHEMATICA BOHEMICA, Vol. 127, No. 2, pp. 243-250 (2002)

Problems involving $p$-Laplacian type
equations and measures

Tero Kilpeläinen

Tero Kilpeläinen, University of Jyväskylä, Department of Mathematics, P. O. Box 35, 40351 Jyväskylä, Finland, e-mail:

Abstract: In this paper I discuss two questions on $p$-Laplacian type operators: I characterize sets that are removable for Hölder continuous solutions and then discuss the problem of existence and uniqueness of solutions to $-\div (|\nabla u|^{p-2}\nabla u)=\mu $ with zero boundary values; here $\mu $ is a Radon measure. The joining link between the problems is the use of equations involving measures.

Keywords: $p$-Laplacian, removable sets

Classification (MSC2000): 35J60, 35J70

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