Search results for "J15"

showing 2 items of 22 documents

Hölder regularity for stochastic processes with bounded and measurable increments

2022

We obtain an asymptotic Hölder estimate for expectations of a quite general class of discrete stochastic processes. Such expectations can also be described as solutions to a dynamic programming principle or as solutions to discretized PDEs. The result, which is also generalized to functions satisfying Pucci-type inequalities for discrete extremal operators, is a counterpart to the Krylov-Safonov regularity result in PDEs. However, the discrete step size $\varepsilon$ has some crucial effects compared to the PDE setting. The proof combines analytic and probabilistic arguments.

todennäköisyyslaskentamatematiikkaApplied Mathematicsp-harmoniousProbability (math.PR)tug-of-war gamesstochastic processdynamic programming principlelocal Hölder estimatesFOS: Mathematicsequations in nondivergence formp-Laplace35B65 35J15 60H30 60J10 91A50Mathematical PhysicsAnalysisAnalysis of PDEs (math.AP)stokastiset prosessit
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Constant sign and nodal solutions for parametric anisotropic $(p, 2)$-equations

2021

We consider an anisotropic ▫$(p, 2)$▫-equation, with a parametric and superlinear reaction term.Weshow that for all small values of the parameter the problem has at least five nontrivial smooth solutions, four with constant sign and the fifth nodal (sign-changing). The proofs use tools from critical point theory, truncation and comparison techniques, and critical groups. Spletna objava: 9. 9. 2021. Abstract. Bibliografija: str. 1076.

udc:517.9electrorheological fluidsElectrorheological fluidMaximum principleMathematics - Analysis of PDEsSettore MAT/05 - Analisi MatematicaFOS: Mathematicsconstant sign and nodal solutionsAnisotropyanisotropic operators regularity theory maximum principle constant sign and nodal solutions critical groups variable exponent electrorheological fluidsParametric statisticsMathematicsvariable exponentVariable exponentApplied MathematicsMathematical analysisudc:517.956.2regularity theoryAnisotropic operatorsanisotropic operatorsTerm (time)Primary: 35J20 35J60 35J92 Secondary: 47J15 58E05maximum principleConstant (mathematics)critical groupsAnalysisAnalysis of PDEs (math.AP)Sign (mathematics)
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