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Critical exponents for semilinear equations of mixed elliptic‐hyperbolic and degenerate types
Author(s) -
Lupo Daniela,
Payne Kevin R.
Publication year - 2003
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/cpa.3031
Subject(s) - mathematics , degenerate energy levels , sobolev space , critical exponent , nonlinear system , exponent , mathematical analysis , boundary (topology) , type (biology) , dirichlet boundary condition , dirichlet distribution , pure mathematics , boundary value problem , scaling , geometry , physics , ecology , linguistics , philosophy , quantum mechanics , biology
For semilinear Gellerstedt equations with Tricomi, Goursat or Dirichlet boundary conditions we prove Pohozaev type identities and derive non existence results that exploit an invariance of the linear part with respect to certain nonhomogeneous dilations. A critical exponent phenomenon of power type in the nonlinearity is exhibited in these mixed elliptic hyperbolic or degenerate settings where the power is one less than the critical exponent in a relevant Sobolev imbedding. © 2002 Wiley Periodicals, Inc.