JournalsaihpcVol. 28, No. 6pp. 775–795

Superharmonic functions are locally renormalized solutions

  • Tero Kilpeläinen

    Department of Mathematics and Statistics, P.O. Box 35, FI-40014 University of Jyväskylä, Finland

  • Tuomo Kuusi

    Aalto University, Institute of Mathematics, P.O. Box 11100, FI-00076 Aalto, Finland

  • Anna Tuhola-Kujanpää

    Department of Mathematics and Statistics, P.O. Box 35, FI-40014 University of Jyväskylä, Finland
Superharmonic functions are locally renormalized solutions cover
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Abstract

We show that different notions of solutions to measure data problems involving p-Laplace type operators and nonnegative source measures are locally essentially equivalent. As an application we characterize singular solutions of multidimensional Riccati type partial differential equations.

Cite this article

Tero Kilpeläinen, Tuomo Kuusi, Anna Tuhola-Kujanpää, Superharmonic functions are locally renormalized solutions. Ann. Inst. H. Poincaré Anal. Non Linéaire 28 (2011), no. 6, pp. 775–795

DOI 10.1016/J.ANIHPC.2011.03.004