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Fine topology and fine trace on the boundary associated with a class of semilinear differential equations
Author(s) -
Dynkin E. B.,
Kuznetsov S. E.
Publication year - 1998
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/(sici)1097-0312(199808)51:8<897::aid-cpa2>3.0.co;2-0
Subject(s) - mathematics , trace (psycholinguistics) , class (philosophy) , boundary (topology) , trace class , topology (electrical circuits) , mathematical analysis , differential equation , computer science , combinatorics , philosophy , linguistics , artificial intelligence , hilbert space
We investigate the set of all positive solutions ofa semilinear equation Lu = ψ( u ) where L is a second‐orderelliptic differential operator in a domain E of ℝ d or, more generally,in a Riemannian manifold and ψ belongs to a wide class ofconvex functions that contains ψ( u ) = u α for all α > 1.We define boundary singularities of a solution u in terms of points ofrapid growth of the right derivative ψ + ( u ), we introduce a finetopology and a fine trace of u on the Martinboundary, and we construct the minimal solution for every possiblevalue of this trace. © 1998 John Wiley & Sons, Inc.