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Superharmonic functions are locally renormalized solutions

Tero KilpeläinenAnna Tuhola-kujanpääTuomo Kuusi

subject

Partial differential equationSubharmonic functionApplied Mathematicsta111Mathematical analysisType (model theory)Measure (mathematics)Parabolic partial differential equationPotential theoryMathematical PhysicsAnalysisMathematics

description

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.

yearjournalcountryeditionlanguage
2011-01-01Annales de l'Institut Henri Poincare (C) Non Linear Analysis
10.1016/j.anihpc.2011.03.004http://dx.doi.org/10.1016/j.anihpc.2011.03.004