Moser functions and fractional Moser-Trudinger type inequalities

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• 作者：Ali Hyder ^{ali.hyder@unibas.ch" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Fractional Moser&ndash ; Trudinger inequalities ; Nonlocal equations
• 刊名：Nonlinear Analysis
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：146
• 期：Complete
• 页码：185-210
• 全文大小：756 K

文摘

We improve the sharpness of some fractional Moser–Trudinger type inequalities, particularly those studied by Lam–Lu and Martinazzi. As an application, improving upon works of Adimurthi and Lakkis, we prove the existence of weak solutions to the problem with Dirichlet boundary condition, for any domain 1961&_mathId=si2.gif&_user=111111111&_pii=S0362546X16301961&_rdoc=1&_issn=0362546X&md5=9b8bdc6525066e1110417b31eff7f24b" title="Click to view the MathML source">Ω$\Omega$ in 1961&_mathId=si3.gif&_user=111111111&_pii=S0362546X16301961&_rdoc=1&_issn=0362546X&md5=a1673a424d13fad38cbc62462af3ccae" title="Click to view the MathML source">Rⁿ${\mathbb{R}}^n$ with finite measure. Here 1961&_mathId=si4.gif&_user=111111111&_pii=S0362546X16301961&_rdoc=1&_issn=0362546X&md5=dab42b0bb8d2b5c489556e82b9be7f39" title="Click to view the MathML source">λ₁${\lambda }_1$ is the first eigenvalue of 1961&_mathId=si5.gif&_user=111111111&_pii=S0362546X16301961&_rdoc=1&_issn=0362546X&md5=7f6ada85ad30d557b471169b2591fa5e">1961-si5.gif">${(-\Delta )}^{\frac{n}{2}}$ on 1961&_mathId=si2.gif&_user=111111111&_pii=S0362546X16301961&_rdoc=1&_issn=0362546X&md5=9b8bdc6525066e1110417b31eff7f24b" title="Click to view the MathML source">Ω$\Omega$.