Bruno Franchi, Ermanno Lanconelli, James Serrin (1985)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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In this paper we describe some existence and uniqueness theorems for radial ground states of a class of quasilinear elliptic equations. In particular, the mean curvature operator and the degenerate Laplace operator are considered.
Maurizio Chicco (1983)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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We give some counterexamples concerning the regularity of the first (resp. second) derivatives of solutions of linear second order elliptic partial differential equations in divergence form (resp. in non-divergence form).
Maurizio Chicco (1983)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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We give some counterexamples concerning the regularity of the first (resp. second) derivatives of solutions of linear second order elliptic partial differential equations in divergence form (resp. in non-divergence form).
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Stefano Mortola, Sergio Steffè (1985)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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In this note we study the periodic homogenization problem for a particular bidimensional selfadjoint elliptic operator of the second order. Theoretical and numerical considerations allow us to conjecture explicit formulae for the coefficients of the homogenized operator.
Stefano Mortola, Sergio Steffè (1985)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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In this note we study the periodic homogenization problem for a particular bidimensional selfadjoint elliptic operator of the second order. Theoretical and numerical considerations allow us to conjecture explicit formulae for the coefficients of the homogenized operator.
Lamberto Cesari (1976)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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Under sole qualitative hypotheses in the large the author has proved the existence of equibounded solutions to nonlinear operational equations in a Hilbert space when a parameter describes an interval containing a point of resonance. Applications have been made to problems of periodic solutions, and to elliptic problems.
Francesco Chiacchio (2001)
Bollettino dell'Unione Matematica Italiana
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Monica Musso (1998)
Bollettino dell'Unione Matematica Italiana
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S. Campanato (1967)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Katiuscia Cerqueti (2000)
Bollettino dell'Unione Matematica Italiana
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Italo Capuzzo Dolcetta (2001)
Bollettino dell'Unione Matematica Italiana
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This is the expanded text of a lecture about viscosity solutions of degenerate elliptic equations delivered at the XVI Congresso UMI. The aim of the paper is to review some fundamental results of the theory as developed in the last twenty years and to point out some of its recent developments and applications.