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Classification and probabilistic representation of the positive solutions of a semilinear elliptic equation / / Benoît Mselati
| Classification and probabilistic representation of the positive solutions of a semilinear elliptic equation / / Benoît Mselati |
| Autore | Mselati Benoît <1977-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2004 |
| Descrizione fisica | 1 online resource (146 p.) |
| Disciplina | 515/.353 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico | Differential equations, Elliptic |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0396-X |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""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. Bibliography""; ""Notation index""; ""Subject index""; ""A""; ""B""; ""C""; ""D""; ""E""; ""F""; ""G""; ""H""; ""I""; ""L""; ""M""; ""N""; ""P""; ""R""; ""S""; ""T"" |
| Record Nr. | UNINA-9910480524503321 |
Mselati Benoît <1977->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2004 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Classification and probabilistic representation of the positive solutions of a semilinear elliptic equation / / Benoît Mselati
| Classification and probabilistic representation of the positive solutions of a semilinear elliptic equation / / Benoît Mselati |
| Autore | Mselati Benoît <1977-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2004 |
| Descrizione fisica | 1 online resource (146 p.) |
| Disciplina | 515/.353 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico | Differential equations, Elliptic |
| ISBN | 1-4704-0396-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""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. Bibliography""; ""Notation index""; ""Subject index""; ""A""; ""B""; ""C""; ""D""; ""E""; ""F""; ""G""; ""H""; ""I""; ""L""; ""M""; ""N""; ""P""; ""R""; ""S""; ""T"" |
| Record Nr. | UNINA-9910788746103321 |
|
Mselati Benoît <1977->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2004 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Classification and probabilistic representation of the positive solutions of a semilinear elliptic equation / / Benoît Mselati
| Classification and probabilistic representation of the positive solutions of a semilinear elliptic equation / / Benoît Mselati |
| Autore | Mselati Benoît <1977-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2004 |
| Descrizione fisica | 1 online resource (146 p.) |
| Disciplina | 515/.353 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico | Differential equations, Elliptic |
| ISBN | 1-4704-0396-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""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. Bibliography""; ""Notation index""; ""Subject index""; ""A""; ""B""; ""C""; ""D""; ""E""; ""F""; ""G""; ""H""; ""I""; ""L""; ""M""; ""N""; ""P""; ""R""; ""S""; ""T"" |
| Record Nr. | UNINA-9910808074203321 |
|
Mselati Benoît <1977->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2004 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||