Elliptic partial differential equations with almost-real coefficients / / Ariel Barton

• Record Nr.: UNINA9910480640103321
• Autore: Barton Ariel <1982->
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , 2012; ©2012
• ISBN: 0-8218-9875-2
• Descrizione fisica: 1 online resource (106 p.)
• Collana: Memoirs of the American Mathematical Society, , 1947-6221 ; ; Volume 223, Number 1051
• Disciplina: 515/.3533
• Soggetti: Differential equations, Elliptic; Differential equations, Partial; Electronic books.
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: "May 2013 , Volume 223, Number 1051 (fifth of 5 numbers)."
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: ""Contents""; ""Abstract""; ""Chapter 1. Introduction""; ""1.1. History""; ""Chapter 2. Definitions and the Main Theorem""; ""2.1. Geometric definitions""; ""2.2. Definitions of function spaces""; ""2.3. Layer potentials""; ""2.4. The main theorem""; ""2.5. Additional definitions""; ""Chapter 3. Useful Theorems""; ""3.1. Nontangential maximal functions""; ""3.2. Bounds on solutions""; ""3.3. Existence results""; ""3.4. Preliminary uniqueness results""; ""3.5. The Neumann and regularity problems in unusual domains""; ""Chapter 4. The Fundamental Solution""; ""4.1. A fundamental solution exists""""4.2. Uniqueness of the fundamental solution""; ""4.3. Symmetry of the fundamental solution""; ""4.4. Conjugates to the fundamental solution""; ""4.5. Calderón-Zygmund kernels""; ""4.6. Analyticity""; ""Chapter 5. Properties of Layer Potentials""; ""5.1. Limits of layer potentials and the adjoint formulas""; ""Chapter 6. Boundedness of Layer Potentials""; ""6.1. Proof for a small Lipschitz constant: preliminary remarks""; ""6.2. A B for the TB theorem""; ""6.3. Weak boundedness of operators""; ""6.4. The adjoint inequalities""; ""6.5. Proof for a small Lipschitz constant: final remarks""""6.6. Buildup to arbitrary special Lipschitz domains""; ""6.7. Patching: special ; Lipschitz domains to bounded Lipschitz domains""; ""Chapter 7. Invertibility of Layer Potentials and Other Properties""; ""7.1. Nontangential maximal functions of layer potentials""; ""7.2. Jump relations""; ""7.3. Layer potentials on Hardy spaces""; ""7.4. Invertibility of layer potentials""; ""Chapter 8. Uniqueness of Solutions""; ""8.1. Counterexamples to uniqueness""; ""8.2. Uniqueness results""; ""Chapter 9. Boundary Data in Hardy spaces""; ""9.1. Solutions with boundary data in Hardy spaces""""9.2. Invertibility of layer potentials""; ""Chapter 10. Concluding Remarks""; ""10.1. Converses""; ""Bibliography""