Results 61 to 70 of about 1,128 (190)

Trace theorems on Herz-Morrey spaces with applications to Sobolev type inequalities

Boundary Value Problems
In this paper, we prove the trace theorems in the setting of Riesz potential operator for Herz-Morrey spaces and present some examples to illustrate the optimality of certain parametric conditions.
Abdul Hamid Ganie, Ghada Ali Basendwah, Babar Sultan, Najla M. Aloraini, Ioan-Lucian Popa   +4 more
doaj   +1 more source

Inverse problems for semilinear elliptic PDE with a general nonlinearity a(x,u)$a(x,u)$

Transactions of the London Mathematical Society, Volume 13, Issue 1, December 2026.
Abstract This article studies the inverse problem of recovering a nonlinearity in an elliptic equation Δu+a(x,u)=0$\Delta u + a(x,u) = 0$ from boundary measurements of solutions. Previous results based on first‐order linearization achieve this under a sign condition on ∂ua(x,u)$\partial _u a(x,u)$, and results based on higher order linearization ...
David Johansson, Janne Nurminen, Mikko Salo   +2 more
wiley   +1 more source

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

On Compressible Fluid Flows of Forchheimer‐Type in Rotating Heterogeneous Porous Media

Mathematical Methods in the Applied Sciences, Volume 49, Issue 13, Page 15010-15055, 15 September 2026.
ABSTRACT We study the dynamics of compressible fluids in rotating heterogeneous porous media. The fluid flow is of Forchheimer‐type and is subject to a mixed mass and volumetric flux boundary condition. The governing equations are reduced to a nonlinear partial differential equation for the pseudo‐pressure.
Emine Celik, Luan Hoang, Thinh Kieu
wiley   +1 more source

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

Sharp Hardy–Sobolev inequalities

Comptes Rendus. Mathématique, 2004
Let Ω be a smooth bounded domain in R N , N ⩾ 3
Filippas, S., Maz'ya, V. G., Tertikas, A.   +2 more
openaire   +2 more sources

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

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

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