English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

We prove that for every $p > 1$ and for every potential $V \in L^p$, anynonnegative function satisfying $-\Delta u + V u \ge 0$ in an open connectedset of $\mathbb{R}^N$ is either identically zero or its level set $\{u = 0\}$has zero $W^{2, p}$ capacity. This gives an affirmative answer to an openproblem of B\'enilan and Brezis concerning a bridge betweenSerrin-Stampacchia's strong maximum principle for $p > \frac{N}{2}$ andAncona's strong maximum principle for $p = 1$. The proof is based on theconstruction of suitable test functions depending on the level set $\{u = 0\}$and on the existence of solutions of the Dirichlet problem for theSchr\"odinger operator with diffuse measure data.

Strong maximum principle for Schr\"odinger operators with singular potential