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: terok@math.jyu.fi

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

Full text of the article:

[Previous Article] [Next Article] [Contents of this Number]
© 2005 ELibM and FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition