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Estimates of Heat Kernels for a Class of Second‐Order Elliptic Operators with Applications to Semi‐Linear Inequalities in Exterior Domains
Author(s) -
Kondratiev Vladimir,
Liskevich Vitali,
Sobol Zeev,
Us Oleksiy
Publication year - 2004
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610703004824
Subject(s) - mathematics , class (philosophy) , order (exchange) , parabolic partial differential equation , mathematical analysis , heat equation , gaussian , nonlinear system , elliptic partial differential equation , partial differential equation , computer science , physics , finance , quantum mechanics , artificial intelligence , economics
Fundamental solutions to second‐order parabolic and elliptic equations with lower‐order terms are studied. New sufficient conditions on the coefficients of the lower‐order terms are given that guarantee the validity of two‐sided Gaussian bounds on the fundamental solution to the parabolic equation, locally and globally in time. As an application, the problem of existence and non‐existence of positive solutions to a class of semi‐linear equations is studied.