Existence and uniqueness of $$\infty $$∞-harmonic functions under assumption of $$\infty $$∞-Poincaré inequality
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DOI: 10.1007/s00208-018-1747-z
Abstract: Given a complete metric measure space whose measure is doubling and supports an $$\infty $$∞-Poincaré inequality, and a bounded domain $$\Omega $$Ω in such a space together with a Lipschitz function $$f:\partial \Omega \rightarrow {\mathbb… read more here.
Keywords: infty; infty harmonic; space; poincar inequality ... See more keywords
A Remark on the Steklov–Poincaré Inequality
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DOI: 10.1134/s0001434621070233
Abstract: In an $$n$$ -dimensional bounded domain $$\Omega_n$$ , $$n\ge 2$$ , we prove the Steklov–Poincare inequality with the best constant in the case where $$\Omega_n$$ is an $$n$$ -dimensional ball. We also consider the case… read more here.
Keywords: steklov poincar; remark steklov; steklov; inequality ... See more keywords