Search results for "p-Parabolic"

showing 3 items of 3 documents

On the second-order regularity of solutions to the parabolic p-Laplace equation

2022

AbstractIn this paper, we study the second-order Sobolev regularity of solutions to the parabolic p-Laplace equation. For any p-parabolic function u, we show that $$D(\left| Du\right| ^{\frac{p-2+s}{2}}Du)$$ D ( D u p - 2 + s 2 D u ) exists as a function and belongs to $$L^{2}_{\text {loc}}$$ L loc 2 with $$s>-1$$ s > - 1 and $$1<p<\infty $$ 1 < p < ∞ . The range of s is sharp.

osittaisdifferentiaaliyhtälötp-parabolic functionstime derivativeSobolev regularityMathematics::Analysis of PDEsfundamental inequalityWeak solutionsMathematics (miscellaneous)Fundamental inequalityweak solutionsGRADIENT111 MathematicsTime derivativeEQUIVALENCE
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Irregular Time Dependent Obstacles

2010

Abstract We study the obstacle problem for the Evolutionary p-Laplace Equation when the obstacle is discontinuous and does not have regularity in the time variable. Two quite different procedures yield the same solution.

Yield (engineering)Parabolic obstacle problemVariational inequalities35K55 31B15 31B05Irregular obstacleLeast solutionComputer Science::RoboticsParabolic balayageLavrentiev phenomenonMathematics - Analysis of PDEsSupersolutionp-ParabolicObstacleVariational inequalityObstacle problemFOS: MathematicsApplied mathematicsTime variablePotentialAnalysisAnalysis of PDEs (math.AP)Mathematics
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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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