Results 61 to 70 of about 259 (139)

EQUIVALENCE OF SOBOLEV INEQUALITIES AND LIEB-THIRRING INEQUALITIES [PDF]

XVIth International Congress on Mathematical Physics, 2010
We show that, under very general definitions of a kinetic energy operator $T$, the Lieb-Thirring inequalities for sums of eigenvalues of $T-V$ can be derived from the Sobolev inequality appropriate to that choice of $T$.
Frank, Rupert L., Lieb, Elliott H., Seiringer, Robert   +2 more
openaire   +3 more sources

Remarks on the Maximal Regularity for Parabolic Boundary Value Problems With Inhomogeneous Data

Mathematical Methods in the Applied Sciences, Volume 49, Issue 13, Page 15316-15326, 15 September 2026.
ABSTRACT Inspired by Ogawa‐Shimizu and Chen‐Liang‐Tsai on the second and first order derivative estimates of solutions of the heat equation in the upper half space with boundary data in homogeneous Besov spaces, we extend the estimates to any order of derivatives, including fractional derivatives.
Hui Chen, Su Liang, Tai‐Peng Tsai
wiley   +1 more source

A Geometrically Regularized Gradient‐Damage Model With Orthogonality‐Based Energy Split for Dynamic Anisotropic Compression‐Shear Fracture

International Journal for Numerical and Analytical Methods in Geomechanics, Volume 50, Issue 13, Page 5185-5212, September 2026.
ABSTRACT This study proposes a novel geometrically regularized gradient‐damage model for simulating dynamic mixed‐mode fracture in orthotropic materials with tension–compression asymmetry. In this model, a thermodynamic framework is formulated by incorporating damage dissipation into internal energy evolution, from which the constitutive relation and ...
Hui Li, Shanyong Wang
wiley   +1 more source

Uniqueness for Neumann Problems for Nonlinear Elliptic Equations With Lower Order Terms

Mathematische Nachrichten, Volume 299, Issue 8, Page 1956-1982, August 2026.
ABSTRACT In this paper, we prove uniqueness results for weak solutions to a class of Neumann problems, whose prototype is λ(1+u2)(p−2)/2u−div((1+|∇u|2)(p−2)/2∇u)−div(c(x)(1+|u|2)(τ+1)/2)+b(x)(1+|∇u|2)(σ+1)/2=finΩ(1+|∇u|2)(p−2)/2∇u+c(x)(1+|u|2)(τ+1)/2)·n̲=0on∂Ω,$$\begin{equation*} {\begin{cases} {}\lambda {(1+ u^2)}^{(p-2)/2}u-{\operatorname{div}}({(1+|\
Maria Francesca Betta, Olivier Guibé, Anna Mercaldo, Maria Rosaria Posteraro   +3 more
wiley   +1 more source

Logarithmic Sobolev inequality revisited

Comptes Rendus. Mathématique, 2017
We provide a new characterization of the logarithmic Sobolev inequality.
Nguyen, Hoai-Minh, Squassina, Marco
openaire   +6 more sources

Existence of Solution for Two Classes of Quasilinear Systems Defined on a Nonreflexive Orlicz–Sobolev Spaces

Mathematical Methods in the Applied Sciences, Volume 49, Issue 12, Page 13324-13360, August 2026.
ABSTRACT This paper proves the existence of nontrivial solution for two classes of quasilinear systems of the type −ΔΦ1u=Fu(x,u,v)+λRu(x,u,v)inΩ−ΔΦ2v=−Fv(x,u,v)−λRv(x,u,v)inΩu=v=0on∂Ω$$ \left\{\begin{array}{l}\hfill -{\Delta}_{\Phi_1}u={F}_u\left(x,u,v\right)+\lambda {R}_u\left(x,u,v\right)\kern0.1832424242424242em \mathrm{in}\kern0.3em \Omega ...
Lucas da Silva, Marco Souto
wiley   +1 more source

On quantum Sobolev inequalities

Journal of Functional Analysis
27 pages. v2: added references, Morrey inequalities and comments on Riesz transforms. v3: typos corrected, added parallel and references to the skew information (Cor 2.2), comparison with commutators with complex exponentials (Prop 2.3) and an appendix on the quantum fractional ...
openaire   +4 more sources

Shape Derivatives of the Eigenvalues of the de Rham Complex for Lipschitz Deformations and Variable Coefficients: Part II

Mathematical Methods in the Applied Sciences, Volume 49, Issue 12, Page 14244-14265, August 2026.
ABSTRACT In this second part of our series of papers, we develop an abstract framework suitable for de Rham complexes that depend on a parameter belonging to an arbitrary Banach space. Our primary focus is on spectral perturbation problems and the differentiability of eigenvalues with respect to perturbations of the involved parameters. As a byproduct,
Pier Domenico Lamberti, Dirk Pauly, Michele Zaccaron   +2 more
wiley   +1 more source

Linear Toroidal‐Inertial Waves on A Differentially Rotating Sphere with Application to Helioseismology: Modeling, Forward and Inverse Problems

Mathematical Methods in the Applied Sciences, Volume 49, Issue 12, Page 14122-14148, August 2026.
ABSTRACT This paper develops a mathematical framework for interpreting observations of solar inertial waves in an idealized setting. Under the assumption of purely toroidal linear waves on the sphere, the stream function of the flow satisfies a fourth‐order scalar equation.
Tram Thi Ngoc Nguyen, Damien Fournier, Laurent Gizon, Thorsten Hohage   +3 more
wiley   +1 more source

Sharp trace Hardy–Sobolev inequalities and fractional Hardy–Sobolev inequalities

Journal of Functional Analysis, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources