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Uniqueness of solutions to degenerate parabolic and elliptic equations in weighted Lebesgue spaces
Author(s) -
Punzo Fabio
Publication year - 2013
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201200040
Subject(s) - mathematics , uniqueness , degenerate energy levels , boundary (topology) , mathematical analysis , lp space , elliptic operator , boundary value problem , class (philosophy) , lebesgue integration , operator (biology) , parabolic partial differential equation , pure mathematics , partial differential equation , banach space , physics , quantum mechanics , transcription factor , gene , biochemistry , chemistry , repressor , artificial intelligence , computer science
We investigate uniqueness for degenerate parabolic and elliptic equations in the class of solutions belonging to weighted Lebesgue spaces and not satisfying any boundary condition. The uniqueness result that we provide relies on the existence of suitable positive supersolutions of the adjoint equations. Under proper assumptions on the behavior at the boundary of the coefficients of the operator, such supersolutions are constructed, mainly using the distance function from the boundary.