Pohozaev's Identity from a Variational Viewpoint
Copyright policy )Pohozaev's Identity from a Variational Viewpoint
1. INTRODUCTIONIn1965S.Pohozaevpublishedapaper[5]inwhichheprovedthenonex-istenceofpositivesolutionstosomesemilinearscalarequationswithsuper-critical growth in a given starshaped domain. His proof is based on anidentity,whichisnowadayswellknownas“Pohozaev’sidentity.”Inthisarticlewegiveaninterpretationofthisidentityfromtheviewpointofthecalculusofvariations.Weintroducethefunctionalforwhichacriticalpoint is the solution to the semilinear equation. This functional is of thetypeJ u=12∇ u
- University of Cologne Germany
Variational methods for second-order elliptic equations, Applied Mathematics, Overdetermined systems of PDEs with variable coefficients, Nonlinear elliptic equations, Existence theories for free problems in two or more independent variables, Analysis, Pokhozhaev identity
Variational methods for second-order elliptic equations, Applied Mathematics, Overdetermined systems of PDEs with variable coefficients, Nonlinear elliptic equations, Existence theories for free problems in two or more independent variables, Analysis, Pokhozhaev identity
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