The weighted Hardy constant
| Autor: | Derek W. Robinson |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
31C25
47D07 Complement (group theory) High Energy Physics::Lattice 010102 general mathematics Degenerate energy levels Boundary (topology) 01 natural sciences Combinatorics Mathematics - Analysis of PDEs Optimal constant Hausdorff dimension 0103 physical sciences Domain (ring theory) FOS: Mathematics 010307 mathematical physics 0101 mathematics Convex domain Constant (mathematics) Analysis Mathematics Analysis of PDEs (math.AP) |
| DOI: | 10.48550/arxiv.2103.07848 |
| Popis: | Let $\Omega$ be a domain in $R^d$ and $d_\Gamma$ the Euclidean distance to the boundary $\Gamma$. We investigate whether the weighted Hardy inequality \[ \|d_\Gamma^{\delta/2-1}\varphi\|_2\leq a_\delta\,\|d_\Gamma^{\delta/2}\,(\nabla\varphi)\|_2 \] is valid, with $\delta\geq 0$ and $a_\delta>0$, for all $\varphi\in C_c^1(\Gamma_r)$ and all small $r>0$ where $\Gamma_r=\{x\in\Omega: d_\Gamma(x)1$ but if $\delta\in[0,1\rangle$ then $a_\delta(\Gamma)$ can be strictly larger than $2/|\delta-1|$. Finally we use these results to establish self-adjointness criteria for degenerate elliptic diffusion operators. Comment: This version differs from the earlier one by the correction of various typos, an extended Section 7 and an additional reference |
| Databáze: | OpenAIRE |
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