The shape of extremal functions for Poincaré-Sobolev-type inequalities in a ball

DOI10.1016/j.jfa.2006.01.001zbMath1122.26015arXiv1407.0315OpenAlexW2077163143MaRDI QIDQ2497905

Tobias Weth, Pedro Martins Girão

Publication date: 4 August 2006

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.0315

zbMATH Keywords

symmetryPoincaré inequalitySobolev inequality

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)

Related Items (16)

On the least-energy solutions of the pure Neumann Lane-Emden equation ⋮ Minimal potential results for Schrödinger equations with Neumann boundary conditions ⋮ Radial symmetry of positive solutions to nonlinear polyharmonic Dirichlet problems ⋮ Poincaré trace inequalities in \(BV({\mathbb {B}}^n)\) with non-standard normalization ⋮ On the asymptotic shape of solutions to Neumann problems for non-cooperative parabolic systems ⋮ Minimization problem related to a Lyapunov inequality ⋮ Sharp asymptotic behavior of radial solutions of some planar semilinear elliptic problems ⋮ Properties of solutions to semilinear elliptic problem with Hardy potential ⋮ Balls minimize trace constants in BV ⋮ Antisymmetry of solutions for some weighted elliptic problems ⋮ Symmetry and asymmetry of minimizers of a class of noncoercive functionals ⋮ Least energy nodal solutions of Hamiltonian elliptic systems with Neumann boundary conditions ⋮ Existence, unique continuation and symmetry of least energy nodal solutions to sublinear Neumann problems ⋮ A shape variation result via the geometry of eigenfunctions ⋮ Partial symmetry and existence of least energy solutions to some nonlinear elliptic equations on Riemannian models ⋮ A rearrangement based proof for the existence of extremal functions for the Sobolev-Poincaré inequality on \(B^n\)

Cites Work

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• On the extremal functions of Sobolev-Poincaré inequality
• An optimal Poincaré inequality for convex domains
• Partial symmetry of least energy nodal solutions to some variational problems
• Rearrangements and convexity of level sets in PDE
• Neumann problems of semilinear elliptic equations involving critical Sobolev exponents
• Sur une généralisation de l'inégalité de Wirtinger. (A generalization of Wirtinger's inequality)
• Spherical rearrangements, subharmonic functions, and \(\ast\)-functions in \(n\)-space
• Instability results for reaction-diffusion equations with Neumann boundary conditions
• On the ``hot spots conjecture of J. Rauch
• A symmetry problem related to Wirtinger's and Poincaré's inequality
• Uniqueness of least energy solutions to a semilinear elliptic equation in \(\mathbb{R}^ 2\)
• Partial symmetry and asymptotic behavior for some elliptic variational problems
• A mass-transportation approach to sharp Sobolev and Gagliardo-Nirenberg inequalities.
• Real analyticity and non-degeneracy
• Symmetry results for functions yielding best constants in Sobolev-type inequalities.
• Balls have the worst best Sobolev inequalities
• A note on additional properties of sign changing solutions to superlinear elliptic equations
• Qualitative properties of nodal solutions of semilinear elliptic equations in radially symmetric domains
• On a family of extremum problems and the properties of an integral
• Schrödinger semigroups
• A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
• On the Number of Nodal Domains for Eigenfunctions of Elliptic Differential Operators
• On a Two-Dimensional Elliptic Problem with Large Exponent in Nonlinearity
• On a Kondratiev problem
• SHARP POINCARÉ–SOBOLEV INEQUALITIES AND THE SHORTEST LENGTH OF SIMPLE CLOSED GEODESICS ON A TOPOLOGICAL TWO SPHERE
• ON THE MINIMIZATION OF SYMMETRIC FUNCTIONALS
• An approach to symmetrization via polarization
• Locating the first nodal linein the Neumann problem
• On the ``one-dimensionality of the extremal in the Poincaré inequality in a square

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