Sharp convex Lorentz-Sobolev inequalities
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Publication:537869
DOI10.1007/s00208-010-0555-xzbMath1220.26020OpenAlexW1969646564MaRDI QIDQ537869
Monika Ludwig, Gaoyong Zhang, Jie Xiao
Publication date: 23 May 2011
Published in: Mathematische Annalen (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00208-010-0555-x
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Cites Work
- Unnamed Item
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- \(\mathrm{SL}(n)\) invariant valuations on polytopes
- An asymmetric affine Pólya-Szegő principle
- The Brunn-Minkowski-Firey theory. I: Mixed volumes and the Minkowski problem
- The Schrödinger operator on the energy space: Boundedness and compactness criteria
- The sharp Sobolev and isoperimetric inequalities split twice
- From Brunn-Minkowski to sharp Sobolev inequalities
- Nonlinear ground state representations and sharp Hardy inequalities
- Lorentz-Sobolev spaces and systems of Schrödinger equations in \(\mathbb R^N\)
- On the role of convexity in isoperimetry, spectral gap and concentration
- General \(L_{p}\) affine isoperimetric inequalities
- Affine Moser-Trudinger and Morrey-Sobolev inequalities
- Maximal volume enclosed by plates and proof of the chessboard conjecture
- A sharp inequality of J. Moser for higher order derivatives
- Best constant in Sobolev inequality
- Problèmes isoperimetriques et espaces de Sobolev
- Choquet integrals in potential theory
- Sobolev type embeddings in the limiting case
- Continuous rotation invariant valuations on convex sets
- The isoperimetric theorem for general integrands
- Best constants for Gagliardo-Nirenberg inequalities and applications to nonlinear diffusions.
- Ellipsoids and matrix-valued valuations
- On solvability of two-dimensional \(L_{p}\)-Minkowski problem.
- On the number of solutions to the discrete two-dimensional \(L_{0}\)-Minkowski problem.
- A mass-transportation approach to sharp Sobolev and Gagliardo-Nirenberg inequalities.
- The Brunn-Minkowski inequality for \(p\)-capacity of convex bodies
- On the \(p\)-affine surface area
- The \(L^p\)-Busemann-Petty centroid inequality
- The discrete planar \(L_0\)-Minkowski problem
- The affine Sobolev inequality.
- \(L_ p\) affine isoperimetric inequalities.
- Sharp affine \(L_ p\) Sobolev inequalities.
- The Cramer-Rao inequality for star bodies
- Projection bodies and valuations
- Surface bodies and \(p\)-affine surface area
- On the Christoffel-Minkowski problem of Firey's \(p\)-sum
- On the regularity of solutions to a generalization of the Minkowski problem
- The Brunn-Minkowski-Firey theory. II: Affine and geominimal surface areas
- \(L_p\) Minkowski problem with not necessarily positive data
- Asymmetric affine \(L_p\) Sobolev inequalities
- On the \(L_{p}\) Minkowski problem for polytopes
- Conductor and capacitary inequalities for functions on topological spaces and their applications to Sobolev-type imbeddings
- The \(L_p\)-Minkowski problem and the Minkowski problem in centroaffine geometry
- Espaces d'interpolation et théorème de Soboleff
- Convolution operators and L(p, q) spaces
- Normal and integral currents
- Infinitesimal form boundedness and Trudinger's subordination for the Schrödinger operator
- An elementary proof of sharp Sobolev embeddings
- Blaschke valuations
- Intersection bodies and valuations
- A characterization of Lp intersection bodies
- Inequalities of Hardy–Sobolev Type in Carnot–Carathéodory Spaces
- Crystalline variational problems
- The sharp constant in Hardy's inequality for complement of bounded domain
- The Brunn-Minkowski inequality
- On the $L_{p}$-Minkowski problem
- Fourier transform and Firey projections of convex bodies
- The p-Faber-Krahn Inequality Noted
- Optimal Sobolev norms and the Lp Minkowski problem
- Form boundedness of the general second‐order differential Operator
- A note on L(\infty, q) spaces and Sobolev embeddings
- Isoperimetric Inequalities in Mathematical Physics. (AM-27)
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