Quantitative Sobolev and Hardy Inequalities, and Related Symmetrization Principles
From MaRDI portal
Publication:3613580
DOI10.1007/978-0-387-85648-3_4zbMath1179.26054OpenAlexW202867311MaRDI QIDQ3613580
Publication date: 12 March 2009
Published in: Sobolev Spaces In Mathematics I (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/978-0-387-85648-3_4
Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Inequalities for sums, series and integrals (26D15) Inequalities involving derivatives and differential and integral operators (26D10)
Related Items
Embeddings, Hardy operators and nonlinear problems, Improved interpolation inequalities, relative entropy and fast diffusion equations, Sobolev and Hardy-Littlewood-Sobolev inequalities
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A sharp isoperimetric inequality in the plane
- Symmetrisierung für Funktionen mehrerer reeller Variablen
- Proprietà di alcune classi di funzioni in più variabili
- An improved Hardy-Sobolev inequality in \(W^{1,p}\) and its application to Schrödinger operators
- The perimeter inequality under Steiner symmetrization: cases of equality
- The sharp Sobolev inequality in quantitative form
- Critical Hardy--Sobolev inequalities
- The sharp quantitative Sobolev inequality for functions of bounded variation
- Hardy inequalities with non-standard remainder terms
- A mass transportation approach to quantitative isoperimetric inequalities
- Sobolev inequalities with remainder terms
- Rearrangements of functions, maximization of convex functionals, and vortex rings
- Rearrangements and convexity of level sets in PDE
- On the isoperimetric nature of a rearrangement inequality and its consequences for some variational problems
- Symmetry and related properties via the maximum principle
- A note on the Sobolev inequality
- Best constant in Sobolev inequality
- Symmetrization of functions in Sobolev spaces and the isoperimetric inequality
- Problèmes isoperimetriques et espaces de Sobolev
- Sobolev type embeddings in the limiting case
- Steiner symmetrization is continuous in \(W^{1,p}\)
- 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
- The Hardy inequality and the asymptotic behaviour of the heat equation with an inverse-square potential
- A general rearrangement inequality à la Hardy-Littlewood
- A geometrical version of Hardy's inequality
- Rearrangement inequalities with application to ratios of heat kernels
- Sharp affine \(L_ p\) Sobolev inequalities.
- A Hardy inequality in the half-space
- A general rearrangement inequality for multiple integrals
- Sharp inequalities for functional integrals and traces of conformally invariant operators.
- Minimal rearrangements of Sobolev functions: A new proof.
- Compactness via symmetrization
- An analytical proof of Hardy-like inequalities related to the Dirac operator
- Convex rearrangement: Equality cases in the Pólya-Szegö inequality
- Optimal Sobolev imbeddings involving rearrangement-invariant quasinorms
- Extremal functions for Hardy's inequality with weight
- Dirichlet integrals and Steiner asymmetry
- The sharp quantitative isoperimetric inequality
- A remark on Hardy type inequalities with remainder terms
- Improved Sobolev inequalities on the Heisenberg group
- Rearrangement inequalities for functionals with monotone integrands
- On a question of Brezis and Marcus
- Steiner symmetric extremals in Pólya-Szegő-type inequalities
- A quantitative Sobolev inequality in BV
- Normal and integral currents
- An improved Hardy-Sobolev inequality and its application
- On the best possible remaining term in the Hardy inequality
- A strengthened version of the Hardy-Littlewood inequality
- Sharp Morrey-Sobolev inequalities and the distance from extremals
- A remark on comparison results via symmetrization
- Imbedding theorems of Sobolev type in potential theory.
- A note on limiting cases of sobolev embeddings and convolution inequalities
- Weakly Differentiable Functions
- A quantitative isoperimetric inequality in n-dimensional space.
- Some remarks on Sobolev inequalities
- Symmetric Decreasing Rearrangement Is Sometimes Continuous
- Hardy inequalities with optimal constants and remainder terms
- A unified approach to improved $L^p$ Hardy inequalities with best constants
- On the Lq norm of functions having equidistributed gradients
- Minimal rearrangements, strict convexity and critical points
- Best remainder norms in Sobolev-Hardy inequalities
- A quantitative Pólya-Szegö principle
- Isoperimetric Inequalities in Mathematical Physics. (AM-27)
