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.

Critical exponents for semilinear equations of mixed elliptic-hyperbolic and degenerate types / Daniela Lupo, Kevin R. Payne. - In: COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS. - ISSN 0010-3640. - 56(2003):3(2003), pp. 403-424.

Critical exponents for semilinear equations of mixed elliptic-hyperbolic and degenerate types

Kevin R. Payne
2003

Abstract

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.
Critical exponents, weighted Sobolev spaces, Hardy-Sobolev inequality, equations of mixed and degenerate types
Settore MAT/05 - Analisi Matematica
2003
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/7031
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