Existence and regularity of the solutions to degenerate elliptic equations in Carnot-Carathéodory spaces
| Autor: | Patrizia Di Gironimo, Flavia Giannetti |
|---|---|
| Přispěvatelé: | DI GIRONIMO, P., Giannetti, F. |
| Rok vydání: | 2020 |
| Předmět: |
Dirichlet problem
regularity Algebra and Number Theory Functional analysis 010102 general mathematics Dimension (graph theory) 0211 other engineering and technologies 021107 urban & regional planning 02 engineering and technology Type (model theory) Operator theory 01 natural sciences Dirichlet distribution Combinatorics symbols.namesake Domain (ring theory) symbols 0101 mathematics Lp space Ap weights Hormander vector fields Ap weights Dirichlet problem regularity H ormander vector fields Analysis Mathematics |
| Zdroj: | Banach Journal of Mathematical Analysis. 14:1670-1691 |
| ISSN: | 1735-8787 2662-2033 |
| DOI: | 10.1007/s43037-020-00069-8 |
| Popis: | We deal with existence and regularity for weak solutions to Dirichlet problems of the type $$\begin{aligned} \left\{ \begin{array}{ll} - \mathrm{div} (A(x)Xu) +b(x)Xu + c(x)u=f\quad \hbox {in} \; \varOmega \\ \\ u=0 \quad \quad \hbox {on} \; \partial \varOmega . \end{array} \right. \end{aligned}$$ in a bounded domain $$\varOmega $$ of $${\mathbb {R}}^n, n\ge 2.$$ We assume that the matrix of the coefficients $$A(x)= {^tA(x)}$$ satisfies the anisotropic bounds $$\begin{aligned} \frac{|\xi |^2}{K(x)}\le \langle A(x) \xi , \xi \rangle \le K(x) |\xi |^2\quad \quad \forall \xi \in {\mathbb {R}}^n,\; \hbox {for a.e.} \; x\in \varOmega \end{aligned}$$ with the ellipticity function $$K(x)\in A_2\cap RH_{\tau }$$ , $$\tau $$ opportunely related to the homogeneous dimension. The functions b(x) and c(x) are assumed to belong to some weighted Lebesgue spaces. |
| Databáze: | OpenAIRE |
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