A supercritical Sobolev type inequality in higher order Sobolev spaces and related higher order elliptic problems

DOI10.1016/j.jde.2019.11.014zbMath1441.46027arXiv1905.01864OpenAlexW2944424665WikidataQ126662067 ScholiaQ126662067MaRDI QIDQ2300421

Nguyen Van Hoang, Quoc-Anh Ngô

Publication date: 27 February 2020

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.01864

zbMATH Keywords

sharp constantoptimizersupercritical Sobolev inequalityhigher-order elliptic problems

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Inequalities involving derivatives and differential and integral operators (26D10) Higher-order elliptic equations (35J30)

Related Items (8)

A sequence of weighted Birman-Hardy-Rellich inequalities with logarithmic refinements ⋮ Existence of solution for elliptic equations with supercritical Trudinger–Moser growth ⋮ Optimality of constants in power-weighted Birman-Hardy-Rellich-Type inequalities with logarithmic refinements ⋮ Critical and supercritical Adams' inequalities with logarithmic weights ⋮ Singular supercritical Trudinger-Moser inequalities and the existence of extremals ⋮ Supercritical Moser-Trudinger inequalities and related elliptic problems ⋮ Extremal functions for a supercritical \(k\)-Hessian inequality of Sobolev-type ⋮ A class of supercritical Sobolev type inequalities with logarithm and related elliptic equations

Cites Work

• On supercritical Sobolev type inequalities and related elliptic equations
• Best constants in the Hardy-Rellich inequalities and related improvements
• Polyharmonic boundary value problems. Positivity preserving and nonlinear higher order elliptic equations in bounded domains
• Classification of solutions of higher order conformally invariant equations
• Non-existence of extremals for the Adimurthi-Druet inequality
• Nodal solutions for a supercritical semilinear problem with variable exponent
• Supercritical Moser-Trudinger inequalities and related elliptic problems
• Hardy-Sobolev type inequality and supercritical extremal problem
• Existence for a \(k\)-Hessian equation involving supercritical growth
• The concentration-compactness principle for variable exponent spaces and applications
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• Remarks on the Moser–Trudinger type inequality with logarithmic weights in dimension 𝑁
• Sharp weighted Sobolev and Gagliardo–Nirenberg inequalities on half-spaces via mass transport and consequences

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