An overview on extremals and critical points of the Sobolev inequality in convex cones

DOI10.4171/rlm/995zbMath1522.35002arXiv2204.12812OpenAlexW4381278269MaRDI QIDQ6111620

Alberto Roncoroni

Publication date: 4 August 2023

Published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2204.12812

zbMATH Keywords

convex conesanisotropic elliptic equationsoptimal transportsharp Sobolev inequalityqualitative properties of PDEs

Mathematics Subject Classification ID

Critical exponents in context of PDEs (35B33) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02) Symmetries, invariants, etc. in context of PDEs (35B06) Quasilinear elliptic equations with (p)-Laplacian (35J92) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23)

Related Items

On the critical \(p\)-Laplace equation, Asymptotic behaviors of solutions to quasilinear elliptic equation with Hardy potential and critical Sobolev exponent, Unnamed Item

Cites Work

• Existence and characterization of regions minimizing perimeter under a volume constraint inside Euclidean cones
• Torus action on S^n and sign changing solutions for conformally invariant equations
• Sobolev inequalities with jointly concave weights on convex cones
• Strong stability for the Wulff inequality with a crystalline norm
• The method of moving planes: a quantitative approach
• On a theorem of functional analysis
• Flows and functional inequalities for fractional operators
• Remainder terms in the fractional Sobolev inequality
• Isoperimetric Inequalities for Convex Cones
• Optimal Transport
• Connected components of sets of finite perimeter and applications to image processing
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the isoperimetric problem for radial log-convex densities
• Sharp stability theorems for the anisotropic Sobolev and log-Sobolev inequalities on functions of bounded variation
• Radial symmetry and applications for a problem involving the \(-\Delta_p(\cdot)\) operator and critical nonlinearity in \(\mathbb{R}^N\)
• Weighted isoperimetric inequalities in cones and applications
• Characterization of isoperimetric sets inside almost-convex cones
• Sharp isoperimetric inequalities via the ABP method
• An overdetermined problem for the anisotropic capacity
• Isoperimetry with upper mean curvature bounds and sharp stability estimates
• Remainder terms in a higher order Sobolev inequality
• Boundary regularity of maps with convex potentials. II
• On the shape of liquid drops and crystals in the small mass regime
• Large energy entire solutions for the Yamabe equation
• Overdetermined anisotropic elliptic problems
• Stability theorems for Gagliardo-Nirenberg-Sobolev inequalities: a reduction principle to the radial case
• Nondegeneracy of nodal solutions to the critical Yamabe problem
• Proprietà di alcune classi di funzioni in più variabili
• Overdetermined problems and constant mean curvature surfaces in cones
• A global compactness result for elliptic boundary value problems involving limiting nonlinearities
• A weighted relative isoperimetric inequality in convex cones
• The sharp Sobolev inequality in quantitative form
• The sharp quantitative Sobolev inequality for functions of bounded variation
• The quantitative isoperimetric inequality and related topics
• A priori estimates and application to the symmetry of solutions for critical \(p\)-Laplace equations
• A mass transportation approach to quantitative isoperimetric inequalities
• Serrin-type overdetermined problems: An alternative proof
• A refined Brunn-Minkowski inequality for convex sets
• Conformal deformation of a Riemannian metric to constant scalar curvature
• Sobolev inequalities with remainder terms
• Asymptotic theory of finite dimensional normed spaces. With an appendix by M. Gromov: Isoperimetric inequalities in Riemannian manifolds
• On a conformally invariant elliptic equation on \(R^ n\)
• A note on the Sobolev inequality
• Classification of solutions of some nonlinear elliptic equations
• Equations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire
• Best constant in Sobolev inequality
• Problèmes isoperimetriques et espaces de Sobolev
• Radial symmetry for elliptic boundary-value problems on exterior domains
• A mass-transportation approach to sharp Sobolev and Gagliardo-Nirenberg inequalities.
• A Sobolev inequality with remainder term and critical equations on domains with topology for the polyharmonic operator
• Elliptic partial differential equations of second order
• The sharp quantitative Euclidean concentration inequality
• A sharp quantitative version of Alexandrov's theorem via the method of moving planes
• Gradient stability for the Sobolev inequality: the case \(p\geq 2\)
• Bubbling with \(L^2\)-almost constant mean curvature and an Alexandrov-type theorem for crystals
• Desingularization of Clifford torus and nonradial solutions to the Yamabe problem with maximal rank
• Symmetry of ground states of quasilinear elliptic equations
• Symmetry of ground states of \(p\)-Laplace equations via the moving plane method
• Cauchy-Liouville and universal boundedness theorems for quasilinear elliptic equations and inequalities.
• A selection principle for the sharp quantitative isoperimetric inequality
• Stability for a GNS inequality and the log-HLS inequality, with application to the critical mass Keller-Segel equation
• A sharp stability result for the relative isoperimetric inequality inside convex cones
• Duality and stability for functional inequalities
• Quantitative estimates for almost constant mean curvature hypersurfaces
• Quantitative stability for hypersurfaces with almost constant curvature in space forms
• Doubling nodal solutions to the Yamabe equation in \(\mathbb{R}^N\) with maximal rank
• Sharp gradient stability for the Sobolev inequality
• Sharp stability of Brunn-Minkowski for homothetic regions
• Existence of nonradial positive and nodal solutions to a critical Neumann problem in a cone
• On the sharp stability of critical points of the Sobolev inequality
• Nearly optimal stability for Serrin's problem and the soap bubble theorem
• Symmetry results for critical anisotropic \(p\)-Laplacian equations in convex cones
• A strong maximum principle for some quasilinear elliptic equations
• A note on strong-form stability for the Sobolev inequality
• Serrin's type overdetermined problems in convex cones
• On the stability for Alexandrov's soap bubble theorem
• The sharp Gagliardo-Nirenberg-Sobolev inequality in quantitative form
• Regularity of monotone transport maps between unbounded domains
• Optimal transport for applied mathematicians. Calculus of variations, PDEs, and modeling
• Quantitative stability for the Brunn-Minkowski inequality
• Quantitative stability of the Brunn-Minkowski inequality for sets of equal volume
• The sharp quantitative isoperimetric inequality
• Improved interpolation inequalities, relative entropy and fast diffusion equations
• A quantitative Sobolev inequality in BV
• A symmetry problem in potential theory
• Remark on the preceding paper of Serrin
• The conjectures on conformal transformations of Riemannian manifolds
• Classification of positive \(\mathcal{D}^{1, p}(\mathbb{R}^N)\)-solutions to the critical \(p\)-Laplace equation in \(\mathbb{R}^N\)
• Symmetry of C¹ Solutions of p-Laplace Equations in ℝ^N
• Droplet Minimizers of an Isoperimetric Problem with Long-Range Interactions
• Sets of Finite Perimeter and Geometric Variational Problems
• The Monge–Ampère equation and its link to optimal transportation
• On the Shape of Compact Hypersurfaces with Almost-Constant Mean Curvature
• Stability in geometric and functional inequalities
• Quantitative stability for hypersurfaces with almost constant mean curvature in the hyperbolic space
• Serrin's problem and Alexandrov's Soap Bubble Theorem: enhanced stability via integral identities
• Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth
• The Yamabe problem
• A uniqueness proof for the Wulff Theorem
• Weakly Differentiable Functions
• The isoperimetric inequality
• A Quantitative Analysis of Metrics on $\mathbb{R}^n$ with Almost Constant Positive Scalar Curvature, with Applications to Fast Diffusion Flows
• Wulff shape characterizations in overdetermined anisotropic elliptic problems