Ventcel’ boundary value problems for elliptic Waldenfels operators
| Autor: | Kazuaki Taira |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Strichartz norm Real analysis General Mathematics 010102 general mathematics Mathematics::Analysis of PDEs Type (model theory) Sobolev space 01 natural sciences Maximum principle Complex interpolation method Besov space Interpolation space Boundary value problem Uniqueness 0101 mathematics Waldenfels integral-differential operator Ventcel’ (Wentzell) boundary condition Mathematics |
| Zdroj: | Bollettino dell'Unione Matematica Italiana. 13:213-256 |
| ISSN: | 2198-2759 1972-6724 |
| DOI: | 10.1007/s40574-019-00214-8 |
| Popis: | In this paper we study a class of first-order Ventcel’ boundary value problems for second-order, elliptic Waldenfels integro-differential operators. More precisely, by using real analysis techniques such as Strichartz norms and the complex interpolation method we prove existence and uniqueness theorems in the framework of Sobolev and Besov spaces of $$L^{p}$$ type which extend earlier theorems due to Bony–Courrege–Priouret and Runst–Youssfi to the general degenerate case. Our proof is based on various maximum principles for second-order, elliptic Waldenfels operators with discontinuous coefficients in the framework of $$L^{p}$$ Sobolev spaces. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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