Maximum Principles and Aleksandrov--Bakelman--Pucci Type Estimates for NonLocal Schrödinger Equations with Exterior Conditions

DOI10.1137/18M1171722zbMath1418.35051arXiv1711.09267OpenAlexW2963874535MaRDI QIDQ4633490

József Lörinczi, Anup Biswas

Publication date: 3 May 2019

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.09267

zbMATH Keywords

subordinate Brownian motionBernstein functionprincipal eigenvalue and eigenfunctionantimaximum principlerefined maximum principlenonlocal Schrödinger operatorDirichlet exterior condition problem

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Maximum principles in context of PDEs (35B50) Eigenvalue problems for linear operators (47A75) Boundary value problems for PDEs with pseudodifferential operators (35S15) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53)

Related Items

Ambrosetti-Prodi type results for Dirichlet problems of fractional Laplacian-like operators, Stability of ground state eigenvalues of non-local Schrödinger operators with respect to potentials and applications, Hopf type lemmas for subsolutions of integro-differential equations, Hopf's lemma for viscosity solutions to a class of non-local equations with applications, A study of nonlocal spatially heterogeneous logistic equation with harvesting, On overdetermined problems for a general class of nonlocal operators, On sublevel set estimates and the Laplacian, Faber-Krahn type inequalities and uniqueness of positive solutions on metric measure spaces, Principal eigenvalues of a class of nonlinear integro-differential operators, Potentials for non-local Schrödinger operators with zero eigenvalues, Maximum principles for time-fractional Cauchy problems with spatially non-local components, Absence of embedded eigenvalues for non-local Schrödinger operators

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