Gelfand type elliptic problems under Steklov boundary conditions

Berchio, Elvise; Gazzola, Filippo; Pierotti, Dario

doi:10.1016/j.anihpc.2009.09.011

Berchio, Elvise ; Gazzola, Filippo ; Pierotti, Dario

Annales de l'I.H.P. Analyse non linéaire, Tome 27 (2010) no. 1, pp. 315-335.

Résumé

For a Gelfand type semilinear elliptic equation we extend some known results for the Dirichlet problem to the Steklov problem. This extension requires some new tools, such as non-optimal Hardy inequalities, and discovers some new phenomena, in particular a different behavior of the branch of solutions and three kinds of blow-up for large solutions in critical growth equations. We also show that small values of the boundary parameter play against strong growth of the nonlinear source.

MR Zbl

DOI : 10.1016/j.anihpc.2009.09.011

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     author = {Berchio, Elvise and Gazzola, Filippo and Pierotti, Dario},
     title = {Gelfand type elliptic problems under {Steklov} boundary conditions},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {315--335},
     publisher = {Elsevier},
     volume = {27},
     number = {1},
     year = {2010},
     doi = {10.1016/j.anihpc.2009.09.011},
     mrnumber = {2580512},
     zbl = {1184.35132},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2009.09.011/}
}

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Berchio, Elvise; Gazzola, Filippo; Pierotti, Dario. Gelfand type elliptic problems under Steklov boundary conditions. Annales de l'I.H.P. Analyse non linéaire, Tome 27 (2010) no. 1, pp. 315-335. doi : 10.1016/j.anihpc.2009.09.011. http://www.numdam.org/articles/10.1016/j.anihpc.2009.09.011/

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