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Viscosity solutions to the degenerate oblique derivative problem for fully nonlinear elliptic equations
Author(s) -
Popivanov P.,
Kutev N.
Publication year - 2005
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.200310280
Subject(s) - degenerate energy levels , oblique case , mathematics , viscosity solution , nonlinear system , viscosity , mathematical analysis , derivative (finance) , dirichlet distribution , dirichlet problem , elliptic curve , physics , thermodynamics , boundary value problem , philosophy , linguistics , quantum mechanics , financial economics , economics
In this paper we prove a comparison principle between the semicontinuous viscosity sub‐ and supersolutions of the tangential oblique derivative problem and the mixed Dirichlet–Neumann problem for fully nonlinear elliptic equations. By means of the comparison principle, the existence of a unique viscosity solution is obtained. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)