0000000000077571

AUTHOR

Tuomo Kuusi

showing 2 related works from this author

Superharmonic functions are locally renormalized solutions

2011

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.

Partial differential equationSubharmonic functionApplied Mathematicsta111Mathematical analysisType (model theory)Measure (mathematics)Parabolic partial differential equationPotential theoryMathematical PhysicsAnalysisMathematicsAnnales de l'Institut Henri Poincare (C) Non Linear Analysis
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Variational parabolic capacity

2015

We establish a variational parabolic capacity in a context of degenerate parabolic equations of $p$-Laplace type, and show that this capacity is equivalent to the nonlinear parabolic capacity. As an application, we estimate the capacities of several explicit sets.

p-parabolic equationcapacityApplied Mathematicsta111Mathematical analysisDegenerate energy levelsMathematics::Analysis of PDEsContext (language use)Parabolic cylinder functionType (model theory)Parabolic partial differential equationHeat capacityNonlinear systemdegenerate parabolic equationsnonlinear potential theoryDiscrete Mathematics and CombinatoricsAnalysisComputer Science::Information TheoryMathematicsDiscrete and Continuous Dynamical Systems
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