Moduli of continuity, functional spaces,\break and elliptic boundary value problems. The full regularity spaces Cα0,λ(Ω̅)
| Autor: | Beirão da Veiga Hugo |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Advances in Nonlinear Analysis, Vol 7, Iss 1, Pp 15-34 (2018) |
| Druh dokumentu: | article |
| ISSN: | 2191-9496 2191-950X |
| DOI: | 10.1515/anona-2016-0041 |
| Popis: | Let 𝑳{\boldsymbol{L}} be a second order uniformly elliptic operator, and consider the equation 𝑳u=f{\boldsymbol{L}u=f} under the boundary condition u=0{u=0}. We assume data f in generical subspaces of continuous functions Dω¯{D_{\overline{\omega}}} characterized by a given modulus of continuityω¯(r){\overline{\omega}(r)}, and show that the second order derivatives of the solution u belong to functional spaces Dω^{D_{\widehat{\omega}}}, characterized by a modulus of continuityω^(r){\widehat{\omega}(r)} expressed in terms of ω¯(r){\overline{\omega}(r)}. Results are optimal. In some cases, as for Hölder spaces, Dω^=Dω¯{D_{\widehat{\omega}}=D_{\overline{\omega}}}. In this case we say that full regularity occurs. In particular, full regularity occurs for the new class of functional spaces Cα0,λ(Ω¯){C^{0,\lambda}_{\alpha}(\overline{\Omega})} which includes, as a particular case, the classical Hölder spaces C0,λ(Ω¯)=C00,λ(Ω¯){C^{0,\lambda}(\overline{\Omega})=C^{0,\lambda}_{0}(\overline{\Omega})}. Few words, concerning the possibility of generalizations and applications to non-linear problems, are expended at the end of the introduction and also in the last section. |
| Databáze: | Directory of Open Access Journals |
| Externí odkaz: |
|