تقرير
On the nonexistence of Green's function and failure of the strong maximum principle
العنوان: | On the nonexistence of Green's function and failure of the strong maximum principle |
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المؤلفون: | Orsina, Luigi, Ponce, Augusto C. |
المصدر: | J. Math. Pures Appl. (2019) |
سنة النشر: | 2018 |
المجموعة: | Mathematics |
مصطلحات موضوعية: | Mathematics - Analysis of PDEs, Mathematics - Functional Analysis, 35J10, 35B05, 35B50 (Primary), 31B15, 31B35, 31C15 (Secondary) |
الوصف: | Given any Borel function $V : \Omega \to [0, +\infty]$ on a smooth bounded domain $\Omega \subset \mathbb{R}^{N}$, we establish that the strong maximum principle for the Schr\"odinger operator $-\Delta + V$ in $\Omega$ holds in each Sobolev-connected component of $\Omega \setminus Z$, where $Z \subset \Omega$ is the set of points which cannot carry a Green's function for $- \Delta + V$. More generally, we show that the equation $- \Delta u + V u = \mu$ has a distributional solution in $W_{0}^{1, 1}(\Omega)$ for a nonnegative finite Borel measure $\mu$ if and only if $\mu(Z) = 0$. |
نوع الوثيقة: | Working Paper |
DOI: | 10.1016/j.matpur.2019.06.001 |
URL الوصول: | http://arxiv.org/abs/1808.07267 |
رقم الأكسشن: | edsarx.1808.07267 |
قاعدة البيانات: | arXiv |
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