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Mathematische Zeitschrift, ISSN 0025-5874, 6/2012, Volume 271, Issue 1, pp. 447 - 467
We point out some of the differences between the consequences of p-Poincaré inequality and that of... 
Primary 46E35 | Secondary 30L10 | {{\mathcal{A}}_{\infty}}$$ weights | Poincaré inequalities | Mathematics, general | 31E05 | Mathematics | Thick quasiconvexity | Metric measure spaces | weights
Journal Article
2005, 1st ed., North-Holland mathematical library, ISBN 9780444517951, Volume 67, 606
The book addresses many important new developments in the field. All the topics covered are of great interest to the readers because such inequalities have become a major tool in the analysis of various branches of mathematics... 
Inequalities (Mathematics)
eBook
Proceedings of the American Mathematical Society, ISSN 0002-9939, 09/2015, Volume 143, Issue 9, pp. 4017 - 4028
In various analytical contexts, it is proved that a weak Sobolev inequality implies a doubling property for the underlying measure. 
Subunit metric spaces | Sobolev inequality | Moser iteration | Doubling condition | subunit metric spaces | LOCAL DIRICHLET SPACES | MATHEMATICS, APPLIED | doubling condition | MINIMIZERS | FORMS | LAPLACIAN | MATHEMATICS | PARABOLIC HARNACK INEQUALITIES | REGULARITY | POINCARE INEQUALITIES | HEAT KERNEL
Journal Article
Journal of functional analysis, ISSN 0022-1236, 2010, Volume 259, Issue 8, pp. 2045 - 2072
Journal Article
The Journal of geometric analysis, ISSN 1050-6926, 12/2018, Volume 28, Issue 4, pp. 3522 - 3552
Extremal functions are exhibited in Poincare trace inequalities for functions of bounded variation in the unit ball Bn of the n-dimensional Euclidean spaceRn... 
Isoperimetric inequalities | Functions of bounded variation | Sobolev spaces | Boundary traces | Poincaré inequalities | Sharp constants | ISOPERIMETRIC INEQUALITY | CONSTANT | SOBOLEV INEQUALITIES | MATHEMATICS | BALLS | WORST | EXTREMAL-FUNCTIONS | Poincare inequalities
Journal Article
Revista matemática iberoamericana, ISSN 0213-2230, 2018, Volume 34, Issue 3, pp. 1021 - 1054
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 2019, Volume 294, Issue 1-2, pp. 17 - 49
.... In this paper, we consider an n-Ahlfors regular rectifiable set M subset of Rn+d that satisfies a Poincare-type inequality involving Lipschitz functions and their tangential derivatives... 
Rectifiable set | Bi-Lipschitz image | Ahlfors regular | Carleson-type condition | p-Poincaré inequality | Poincaré-type condition | MATHEMATICS | p-Poincare inequality | Poincare-type condition | SPACES | RICCI CURVATURE | CHORD ARC SURFACES
Journal Article
Journal of theoretical probability, ISSN 1572-9230, 2019, Volume 33, Issue 1, pp. 396 - 427
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 2019, Volume 266, Issue 1, pp. 44 - 69
Let X be a noncomplete metric measure space satisfying the usual (local) assumptions of a doubling property and a Poincaré inequality... 
Newtonian Sobolev space | Lebesgue point | Quasiminimizer | Noncomplete metric space | p-harmonic function | Poincaré inequality | QUASICONTINUITY | QUASIMINIMIZERS | LIPSCHITZ FUNCTIONS | POTENTIAL-THEORY | OPEN SETS | MATHEMATICS | QUASIOPEN | Poincare inequality | HARMONIC-FUNCTIONS
Journal Article
Revista matemática iberoamericana, ISSN 0213-2230, 2014, Volume 30, Issue 1, pp. 109 - 131
By adapting some ideas of M. Ledoux ([12], [13] and [14]) to a sub-Riemannian framework we study Sobolev, Poincare and isoperimetric inequalities associated... 
Isoperimetric inequality | Subelliptic operator | Sobolev inequalities | Poincaré inequality | MATHEMATICS | isoperimetric inequality | Poincare inequality | subelliptic operator | 1ST EIGENVALUE
Journal Article
Mathematical and computer modelling, ISSN 0895-7177, 2010, Volume 52, Issue 3-4, pp. 556 - 566
Journal Article
Communications in Contemporary Mathematics, ISSN 0219-1997, 12/2016, Volume 18, Issue 6, p. 1550086
In this paper, we prove a sharp upper bound for the first nontrivial eigenvalue of the p -Laplacian with Neumann boundary conditions. This applies to convex... 
shape optimization | Nonlinear eigenvalue problems | EIGENVALUE | MATHEMATICS | MATHEMATICS, APPLIED | CONSTANTS | LOWER BOUNDS | POINCARE INEQUALITIES
Journal Article
Positivity, ISSN 1385-1292, 7/2018, Volume 22, Issue 3, pp. 687 - 699
In this paper we prove the Poincaré-type weighted inequality $$\begin{aligned} \Vert v^{1/q} f \Vert _{L^q(\Omega )} \le C \Vert \omega ^{1/p} \nabla f \Vert... 
Convex domain | 26D10 | Change of variables | 35J70 | 35A23 | Mathematics | 35J15 | Poincaré inequality | Operator Theory | Fourier Analysis | Potential Theory | Weights | Fubini’s theorem | Calculus of Variations and Optimal Control; Optimization | Econometrics | Equality | Inequality
Journal Article
Journal of mathematical analysis and applications, ISSN 0022-247X, 2019, Volume 477, Issue 2, pp. 1157 - 1181
In this paper, we establish several Poincaré–Sobolev type inequalities concerning to the Laplace–Beltrami operator Δ... 
Hyperbolic spaces | Decreasing spherical symmetric rearrangement | Sobolev inequality | Adams inequality with exact growth | Poincaré–Sobolev inequality | Adams inequality
Journal Article
The Journal of Geometric Analysis, ISSN 1050-6926, 4/2019, Volume 29, Issue 2, pp. 1608 - 1648
Journal Article
Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, ISSN 0308-2105, 2019, Volume 150, Issue 4, pp. 1699 - 1736
We prove optimal improvements of the Hardy inequality on the hyperbolic space. Here, optimal means that the resulting operator iscriticalin the sense of Devyver, Fraas, and Pinchover (2014... 
optimal Hardy inequality | extremals | Hyperbolic space | MATHEMATICS | MATHEMATICS, APPLIED | RELLICH INEQUALITIES | EQUATIONS | POINCARE INEQUALITIES | RIEMANNIAN-MANIFOLDS | Manifolds | Inequalities | Inequality
Journal Article
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