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Record Nr. |
UNINA9910480524503321 |
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Autore |
Mselati Benoît <1977-> |
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Titolo |
Classification and probabilistic representation of the positive solutions of a semilinear elliptic equation / / Benoît Mselati |
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Pubbl/distr/stampa |
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Providence, Rhode Island : , : American Mathematical Society, , 2004 |
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©2004 |
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ISBN |
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Descrizione fisica |
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1 online resource (146 p.) |
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Collana |
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Memoirs of the American Mathematical Society, , 0065-9266 ; ; Volume 168, Number 798 |
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Disciplina |
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Soggetti |
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Differential equations, Elliptic |
Electronic books. |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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"March 2004, Volume 168, Number 798 (third of 4 numbers)." |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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""Contents""; ""Introduction and statement of the results""; ""Chapter 1. An analytic approach to the equation Î?u = u[sup(2)]""; ""1.1. Parametrization near the boundary of the domain""; ""1.2. Basic facts about linear elliptic PDE's""; ""1.3. The equation Î?u = u[sup(2)]""; ""Chapter 2. A probabilistic approach to the equation Î?u = u[sup(2)]""; ""2.1. Linear elliptic PDE's and Brownian motion""; ""2.2. The Brownian snake""; ""2.3. Stochastic boundary values""; ""2.4. Fine topology and fine trace""; ""2.5. Two key problems""; ""Chapter 3. Lower bounds for solutions"" |
""Main results proved in this chapter""""3.1. Upper bounds for u[sub(K)] in terms of the boundary capacity of K""; ""3.2. Lower bounds for cr-moderate solutions""; ""3.3. Synthesis""; ""Chapter 4. Upper bounds for solutions""; ""Main results proved in this chapter""; ""4.1. The case of a ""strongly star-shaped domain""""; ""4.2. The case of a general domain""; ""4.3. Proof of Proposition 4.1""; ""Chapter 5. The classification and representation of the solutions of Î?u = u[sup(2)] in a domain""; ""5.1. Representation of solutions""; ""5.2. Admissible traces and classification results"" |
""Appendix A. Technical results""""A.1. Parametrization near the boundary""; ""A.2. Estimates for the Green function""; ""A.3. The auxiliary function p""; ""A.4. Proof of Lemma 2.20""; ""Appendix. |
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