Weighted multipolar Hardy inequalities and evolution problems with Kolmogorov operators perturbed by singular potentials
نویسندگان
چکیده
The main results in the paper are weighted multipolar Hardy inequalities style='text-indent:20px;'> \begin{document}$ \begin{equation*} c\int_{\mathbb{R}^N}\sum\limits_{i = 1}^n\frac{\varphi^2}{|x-a_i|^2}\,\mu(x)dx \leq\int_{\mathbb{R}^N}|\nabla \varphi |^2\mu(x)dx+ K\int_{\mathbb{R}^N} \varphi^2\mu(x)dx, \end{equation*} $\end{document} style='text-indent:20px;'>in \begin{document}$ \mathbb{R}^N $\end{document} for any id="M2">\begin{document}$ a suitable Sobolev space, with id="M3">\begin{document}$ 0<c\le c_{o,\mu} $\end{document}, id="M4">\begin{document}$ a_1,\dots,a_n\in id="M5">\begin{document}$ K constant. The weight functions id="M6">\begin{document}$ \mu of quite general type. fits framework Kolmogorov operators defined on smooth id="FE2"> Lu \Delta u+\frac{\nabla \mu}{\mu}\cdot\nabla u, style='text-indent:20px;'>perturbed by inverse square potentials, and related evolution problems. Necessary sufficient conditions existence exponentially bounded time positive solutions to associated initial value problem based inequalities. For constants id="M7">\begin{document}$ c beyond optimal constant id="M8">\begin{document}$ we able show nonexistence solutions.
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ژورنال
عنوان ژورنال: Communications on Pure and Applied Analysis
سال: 2021
ISSN: ['1534-0392', '1553-5258']
DOI: https://doi.org/10.3934/cpaa.2020274