Search results for " 35K20"

showing 2 items of 2 documents

Perron's method for the porous medium equation

2016

O. Perron introduced his celebrated method for the Dirichlet problem for harmonic functions in 1923. The method produces two solution candidates for given boundary values, an upper solution and a lower solution. A central issue is then to determine when the two solutions are actually the same function. The classical result in this direction is Wiener’s resolutivity theorem: the upper and lower solutions coincide for all continuous boundary values. We discuss the resolutivity theorem and the related notions for the porous medium equation ut −∆u = 0

Dirichlet problemApplied MathematicsGeneral Mathematicsta111010102 general mathematicsMathematical analysiscomparison principlePerron methodFunction (mathematics)Primary 35K55 Secondary 35K65 35K20 31C45obstaclesPorous medium equation01 natural sciencesBoundary values010101 applied mathematicsMathematics - Analysis of PDEsHarmonic functionFOS: Mathematics0101 mathematicsPorous mediumPerron methodAnalysis of PDEs (math.AP)Mathematics
researchProduct

Dependence of the layer heat potentials upon support perturbations

2023

We prove that the integral operators associated with the layer heat potentials depend smoothly upon a parametrization of the support of integration. The analysis is carried out in the optimal H\"older setting.

Mathematics - Analysis of PDEsFOS: Mathematics31B10 47G10 35K05 35K20Analysis of PDEs (math.AP)
researchProduct