Search results for "gradient regularity"

showing 2 items of 2 documents

Gradient and Lipschitz Estimates for Tug-of-War Type Games

2021

We define a random step size tug-of-war game and show that the gradient of a value function exists almost everywhere. We also prove that the gradients of value functions are uniformly bounded and converge weakly to the gradient of the corresponding $p$-harmonic function. Moreover, we establish an improved Lipschitz estimate when boundary values are close to a plane. Such estimates are known to play a key role in the higher regularity theory of partial differential equations. The proofs are based on cancellation and coupling methods as well as an improved version of the cylinder walk argument. peerReviewed

osittaisdifferentiaaliyhtälöt91A15 35B65 35J92gradient regularityApplied MathematicsTug of warMathematical analysisstochastic two player zero-sum gameType (model theory)Lipschitz continuityComputational MathematicsMathematics - Analysis of PDEsLipschitz estimateBellman equationtug-of-war with noiseFOS: MathematicsUniform boundednesspeliteoriaAlmost everywherep-LaplaceValue (mathematics)AnalysisAnalysis of PDEs (math.AP)Mathematicsstokastiset prosessit
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Hölder gradient regularity for the inhomogeneous normalized p(x)-Laplace equation

2022

We prove the local gradient Hölder regularity of viscosity solutions to the inhomogeneous normalized p(x)-Laplace equation −Δp(x)Nu=f(x), where p is Lipschitz continuous, inf⁡p>1, and f is continuous and bounded. peerReviewed

viscosity solutionosittaisdifferentiaaliyhtälötnon-divergence form equationHölder gradient regularityinhomogeneous equationApplied Mathematicsnormalized equationp-LaplaceAnalysisJournal of Mathematical Analysis and Applications
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