Matches in SemOpenAlex for { <https://semopenalex.org/work/W3101813935> ?p ?o ?g. }
- W3101813935 abstract "Let $Omegasubsetmathbb{R}^nu$, $nuge 2$, be a $C^{1,1}$ domain whose boundary $partialOmega$ is either compact or behaves suitably at infinity. For $pin(1,infty)$ and $alpha>0$, define [ Lambda(Omega,p,alpha):=inf_{substack{uin W^{1,p}(Omega) unotequiv 0}}dfrac{displaystyle int_Omega |nabla u|^p mathrm{d} x - alphadisplaystyleint_{partialOmega} |u|^pmathrm{d}sigma}{displaystyleint_Omega |u|^pmathrm{d} x}, ] where $mathrm{d}sigma$ is the surface measure on $partialOmega$. We show the asymptotics [ Lambda(Omega,p,alpha)=-(p-1)alpha^{frac{p}{p-1}} - (nu-1)H_mathrm{max}, alpha + o(alpha), quad alphato+infty, ] where $H_mathrm{max}$ is the maximum mean curvature of $partialOmega$. The asymptotic behavior of the associated minimizers is discussed as well. The estimate is then applied to the study of the best constant in a boundary trace theorem for expanding domains, to the norm estimate for extension operators and to related isoperimetric inequalities." @default.
- W3101813935 created "2020-11-23" @default.
- W3101813935 creator A5046730581 @default.
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- W3101813935 date "2017-03-21" @default.
- W3101813935 modified "2023-10-05" @default.
- W3101813935 title "On the p-Laplacian with Robin boundary conditions and boundary trace theorems" @default.
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- W3101813935 doi "https://doi.org/10.1007/s00526-017-1138-4" @default.
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