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Journal of Functional Analysis, ISSN 0022-1236, 06/2016, Volume 270, Issue 11, pp. 4117 - 4151
We prove a trace Hardy type inequality with the best constant on the polyhedral convex cones which generalizes recent results of Alvino et al. and of Tzirakis... 
Logarithmic Hardy trace inequality | Trace Hardy–Sobolev–Maz'ya type inequality | Logarithmic Sobolev trace inequality | Trace Hardy type inequality | Trace Hardy-Sobolev-Maz'ya type inequality | MATHEMATICS | SHARP CONSTANTS | EQUATION
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 06/2016, Volume 270, Issue 12, pp. 4513 - 4539
In this work we establish sharp weighted trace Hardy inequalities with trace remainder terms involving the critical Sobolev exponent corrected by a singular... 
Weighted trace Hardy inequality | Hardy–Sobolev inequality | Fractional Laplacian | Critical Sobolev exponent | Hardy-Sobolev inequality | LAPLACIAN | MATHEMATICS | REGULARITY | EQUATIONS | OPERATORS | EXTENSION PROBLEM
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 08/2018, Volume 146, Issue 8, pp. 3393 - 3402
As our main result we prove a variant of the fractional Hardy-Sobolev-Maz'ya inequality for half spaces. This result contains a complete answer to a recent... 
John domain | Fractional Hardy-Sobolev inequality | Hardy-Sobolev-Maz’ya inequality | MATHEMATICS | MATHEMATICS, APPLIED | MAZYA INEQUALITY | Hardy-Sobolev-Maz'ya inequality
Journal Article
Communications in Mathematical Physics, ISSN 0010-3616, 09/2019
This paper is devoted to the symmetry and symmetry breaking properties of a two-dimensional magnetic Schrödinger operator involving an Aharonov-Bohm magnetic... 
Mathematical Physics | Analysis of PDEs | Mathematics
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 06/2018, Volume 171, pp. 134 - 155
We consider the optimal Hardy–Sobolevinequality on smooth bounded symmetric domains of the Euclidean space without any assumption concerning the “shape” of the... 
Supercritical Hardy–Sobolev inequalities | Analytical approach of the symmetry | Supercritical Hardy–Sobolev elliptic equations | MATHEMATICS | MATHEMATICS, APPLIED | CONSTANTS | Supercritical Hardy-Sobolev elliptic equations | Supercritical Hardy-Sobolev inequalities | MANIFOLDS | SOLID TORUS
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 01/2015, Volume 421, Issue 2, pp. 1869 - 1888
Given a compact Riemannian manifold (M,g) of dimension n≥3, a point x0∈M and s∈(0,2), the Hardy–Sobolev embedding yields the existence of A,B>0 such... 
Optimal inequalities | Hardy–Sobolev inequalities | Compact Riemannian manifolds | Blow-up | Hardy-Sobolev inequalities | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | SYMMETRY | GAGLIARDO-NIRENBERG INEQUALITIES | SHARP CONSTANTS | CONSTANT PROBLEM | EXTREMALS
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 09/2016, Volume 261, Issue 6, pp. 3107 - 3136
We strengthen the classical inequality of C.B. Morrey concerning the optimal Hölder continuity of functions in W1,p when p>n, by replacing the Lp-modulus of... 
Bounded mean oscillation | Hardy–Sobolev inequality | Weighted Sobolev embedding | Hardy–Morrey inequality
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 05/2019, Volume 182, pp. 316 - 349
Let Ω be a domain of Rn, n≥3. The classical Caffarelli–Kohn–Nirenberg inequality rewrites as the following inequality: for any s∈[0,2] and any γ<(n−2)24, there... 
Hardy–Sobolev inequalities | Non linear elliptic critical equations | Non-smooth geometry | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | NONEXISTENCE | ELLIPTIC-EQUATIONS | Hardy-Sobolev inequalities | Geometry | Singularities | Curvature | Smooth boundaries
Journal Article
Communications in Contemporary Mathematics, ISSN 0219-1997, 08/2019, Volume 21, Issue 5, p. 1850028
The existence of optimizers u in the space Ẇ s , p ( ℝ N ) , with differentiability order s ∈   ] 0 , 1 [ , for the Hardy–Sobolev inequality is established... 
decay estimates | fractional (Formula presented.)-Laplacian | concentration-compactness | Fractional Hardy–Sobolev inequality | MATHEMATICS | fractional p-Laplacian | MATHEMATICS, APPLIED | MULTIPLICITY | POSITIVE SOLUTIONS | Fractional Hardy-Sobolev inequality | EQUATION | Equality
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 01/2014, Volume 266, Issue 1, pp. 55 - 66
The paper gives the following improvement of the Trudinger–Moser inequality:(0.1)sup∫Ω|∇u|2dx−ψ(u)⩽1,u∈C0∞(Ω)∫Ωe4πu2dx<∞,Ω∈R2, related to the... 
Spectral gap | Virtual bound state | Singular elliptic operators | Trudinger–Moser inequality | Borderline Sobolev imbeddings | Hardy–Sobolev–Mazya inequality | Remainder terms | Trudinger-Moser inequality | Hardy-Sobolev-Mazya inequality | MATHEMATICS | Equality | Naturvetenskap | Natural Sciences
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 09/2017, Volume 160, pp. 70 - 78
We study a Neumann problem with the Hardy–Sobolev nonlinearity. In boundary singularity case, the impact of the mean curvature at singularity on existence of... 
minimization problem | Neumann problem | Hardy–Sobolev inequality | boundary singularity | MATHEMATICS | MATHEMATICS, APPLIED | EXPONENTS | BEHAVIOR | LEAST-ENERGY SOLUTIONS | CRITICAL GROWTH | SEMILINEAR NEUMANN PROBLEM | Hardy-Sobolev inequality | ELLIPTIC-EQUATIONS | Equality
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 12/2016, Volume 55, Issue 6, pp. 1 - 16
Wang and Ye conjectured in (Adv Math 230:294–320, 2012): Let $$\Omega $$ Ω be a regular, bounded and convex domain in $$\mathbb {R}^{2}$$ R 2 . There exists a... 
35J20 | 42B35 | 46E35 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | MATHEMATICS | MATHEMATICS, APPLIED | NEGATIVE CURVATURE | SPACE H-N | HYPERBOLIC SPACES | OPERATORS | HARDY-SOBOLEV INEQUALITIES | RIEMANNIAN-MANIFOLDS | Equality
Journal Article
Nonlinear Differential Equations and Applications, ISSN 1021-9722, 06/2017, Volume 24, Issue 3, p. 1
We study minimization problems on Hardy-Sobolev type inequality. We consider the case where singularity is in interior of bounded domain Omega subset of R-N.... 
Neumann | Critical exponent | Hardy–Sobolev inequality | Minimization problem | MATHEMATICS, APPLIED | COMPACT RIEMANNIAN-MANIFOLDS | EXPONENTS | Hardy-Sobolev inequality | ELLIPTIC-EQUATIONS | BOUNDARY SINGULARITIES
Journal Article
Journal Article
Advances in Nonlinear Analysis, ISSN 2191-9496, 12/2016, Volume 8, Issue 1, pp. 130 - 143
We consider the Grushin type operator on of the form and derive weighted Hardy–Sobolev type inequalities and weighted Caffarelli–Kohn–Nirenberg type... 
35H20 | weighted Hardy–Sobolev inequality | 26D10 | weighted Caffarelli–Kohn–Nirenberg type inequality | Grushin type operator | MATHEMATICS | MATHEMATICS, APPLIED | THEOREMS | weighted Hardy-Sobolev inequality | weighted Caffarelli-Kohn-Nirenberg type inequality | 1ST-ORDER INTERPOLATION INEQUALITIES
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 02/2013, Volume 264, Issue 3, pp. 837 - 893
We deal with domains with infinite inner radius. More precisely, we introduce a new geometric assumption on an exterior domain Ω⊂Rn; n⩾3 (i.e. complement of... 
Harnack inequality | Hardy–Sobolev inequalities | Unbounded domain | Exterior domain | Distance function | Heat kernel estimates | Critical exponent | Hardy inequalities | Hardy-Sobolev inequalities | BEHAVIOR | CONSTANT | MATHEMATICS | MANIFOLDS | HARNACK INEQUALITIES | EQUATION | SCHRODINGER-OPERATORS
Journal Article
Proceedings of the Royal Society of Edinburgh Section A: Mathematics, ISSN 0308-2105, 02/2017, Volume 147, Issue 1, pp. 1 - 23
We prove a strong optimal Hardy-Sobolev inequality for the twisted Laplacian on C-n. The twisted Laplacian is the magnetic Laplacian for a system of n... 
special Hermite expansion | Hardy-Sobolev inequality | fundamental solution | twisted Laplacian | MATHEMATICS | MATHEMATICS, APPLIED | Mathematics | Laplace transforms | Planes | Magnetic fields | Sobolev space | Optimization | Inequalities
Journal Article
Proceedings of the Japan Academy Series A: Mathematical Sciences, ISSN 0386-2194, 04/2016, Volume 92, Issue 4, pp. 51 - 55
The main purpose of this article is to study the Caffarelli-Kohn-Nirenberg type inequalities (1.2) with p = 1. We show that symmetry breaking of the best... 
Symmetry break | CKN-type inequality | Best constant | Weighted Hardy-Sobolev inequality | MATHEMATICS | symmetry break | weighted Hardy-Sobolev inequality | best constant | EXTREMAL-FUNCTIONS | WEIGHTS | CONSTANT | ELLIPTIC-EQUATIONS | Inequalities (Mathematics) | Research | Mathematical research | Symmetry
Journal Article
Potential Analysis, ISSN 0926-2601, 1/2019, Volume 50, Issue 1, pp. 83 - 105
Let X be a metric space equipped with a doubling measure. We consider weights w(x) = dist(x,E)−α , where E is a closed set in X and α ∈ ℝ $\alpha \in \mathbb... 
Geometry | 42B25 | Potential Theory | Functional Analysis | Assouad dimension | Metric space | 35A23 | Probability Theory and Stochastic Processes | 31E05 | Mathematics | Muckenhoupt weight | Hardy–Sobolev inequality
Journal Article
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