Search results for " 35J15"

showing 5 items of 5 documents

Landis-type conjecture for the half-Laplacian

2023

In this paper, we study the Landis-type conjecture, i.e., unique continuation property from infinity, of the fractional Schrödinger equation with drift and potential terms. We show that if any solution of the equation decays at a certain exponential rate, then it must be trivial. The main ingredients of our proof are the Caffarelli-Silvestre extension and Armitage’s Liouville-type theorem. peerReviewed

Landis conjecture half-Laplacian Caarelli- Silvestre extension Liouville-type theoremosittaisdifferentiaaliyhtälötMathematics - Analysis of PDEsApplied MathematicsGeneral Mathematicsunique continuation propertyPrimary: 35A02 35B40 35R11. Secondary: 35J05 35J15FOS: MathematicsAnalysis of PDEs (math.AP)
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A minimization problem with free boundary and its application to inverse scattering problems

2023

We study a minimization problem with free boundary, resulting in hybrid quadrature domains for the Helmholtz equation, as well as some application to inverse scattering problem.

Mathematics - Analysis of PDEsFOS: MathematicsAnalysis of PDEs (math.AP)35J05 35J15 35J20 35R30 35R35
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Local regularity estimates for general discrete dynamic programming equations

2022

We obtain an analytic proof for asymptotic H\"older estimate and Harnack's inequality for solutions to a discrete dynamic programming equation. The results also generalize to functions satisfying Pucci-type inequalities for discrete extremal operators. Thus the results cover a quite general class of equations.

local Hölder estimateosittaisdifferentiaaliyhtälötABP-estimateApplied MathematicsGeneral Mathematicsp-LaplacianMathematics::Analysis of PDEs35B65 35J15 35J92 91A50elliptic non-divergence form partial differential equation with bounded and measurable coefficientsdynamic programming principleMathematics - Analysis of PDEsHarnack's inequalitytug-of-war with noiseFOS: MathematicsPucci extremal operatorpeliteoriaepäyhtälötAnalysis of PDEs (math.AP)
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Quadrature domains for the Helmholtz equation with applications to non-scattering phenomena

2022

In this paper, we introduce quadrature domains for the Helmholtz equation. We show existence results for such domains and implement the so-called partial balayage procedure. We also give an application to inverse scattering problems, and show that there are non-scattering domains for the Helmholtz equation at any positive frequency that have inward cusps.

metaharmonic functionsmatematiikkapartial balayageyhtälötmean value theoremMathematics::Numerical Analysis35J05 35J15 35J20 35R30 35R35quadrature domainnon-scattering phenomenaMathematics - Analysis of PDEsFOS: MathematicsHelmholtz equationacoustic equationAnalysisAnalysis of PDEs (math.AP)
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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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