Results 71 to 80 of about 27,220 (202)

Degree theory for 4‐dimensional asymptotically conical gradient expanding solitons

Communications on Pure and Applied Mathematics, Volume 79, Issue 5, Page 1151-1298, May 2026.
Abstract We develop a new degree theory for 4‐dimensional, asymptotically conical gradient expanding solitons. Our theory implies the existence of gradient expanding solitons that are asymptotic to any given cone over S3$S^3$ with non‐negative scalar curvature. We also obtain a similar existence result for cones whose link is diffeomorphic to S3/Γ$S^3/\
Richard H. Bamler, Eric Chen
wiley   +1 more source

Certain imbeddings of weighted Sobolev spaces [PDF]

Mathematical Inequalities & Applications, 2003
The authors characterize weight functions for which the weighted Sobolev space \(W^{1,p}(\Omega, d^\beta_M)\) [and also \(W^{1,p}(\Omega, s_0(d_M))\)] is imbedded continuously or compactly into the weighted Lebesgue space \(L^q(\Omega, d^\alpha_M)\) [and also \(L^q(\Omega, s_1(d_M))\)], where \(1\leq q< p< \infty\) and \(M\subset\partial\Omega\).
Jain, Pankaj, Bansal, Bindu, Jain, Pawan K.   +2 more
openaire   +1 more source

Isoperimetric inequalities on slabs with applications to cubes and Gaussian slabs

Communications on Pure and Applied Mathematics, Volume 79, Issue 4, Page 1012-1072, April 2026.
Abstract We study isoperimetric inequalities on “slabs”, namely weighted Riemannian manifolds obtained as the product of the uniform measure on a finite length interval with a codimension‐one base. As our two main applications, we consider the case when the base is the flat torus R2/2Z2$\mathbb {R}^2 / 2 \mathbb {Z}^2$ and the standard Gaussian measure
Emanuel Milman
wiley   +1 more source

Existence and Uniqueness of Mild Solutions for the Damped Burgers Equation in Weighted Sobolev Spaces on the Half Line

International Journal of Analysis and Applications, 2018
This paper addresses an initial boundary value problem for the damped Burgers equation in weighted Sobolev spaces on half line. First, it introduces two normed spaces and present relations between them, which in turn enables us to analysis the existence ...
Mohammadreza Foroutan, Ali Ebadian
doaj   +2 more sources

On Bounds for Norms of Reparameterized ReLU Artificial Neural Network Parameters: Sums of Fractional Powers of the Lipschitz Norm Control the Network Parameter Vector

Mathematical Methods in the Applied Sciences, Volume 49, Issue 4, Page 2135-2160, 15 March 2026.
ABSTRACT It is an elementary fact in the scientific literature that the Lipschitz norm of the realization function of a feedforward fully connected rectified linear unit (ReLU) artificial neural network (ANN) can, up to a multiplicative constant, be bounded from above by sums of powers of the norm of the ANN parameter vector.
Arnulf Jentzen, Timo Kröger
wiley   +1 more source

Embeddings of a Multi-Weighted Anisotropic Sobolev Type Space

Қарағанды университетінің хабаршысы. Математика сериясы
Parameters such as various integral and differential characteristics of functions, smoothness properties of regions and their boundaries, as well as many classes of weight functions cause complex relationships and embedding conditions for multi-weighted
G.Sh. Iskakova, M.S. Aitenova, A.K. Sexenbayeva   +2 more
doaj   +1 more source

Inner‐Layer Asymptotics in Partially Perforated Domains: Coupling Across Flat and Oscillating Interfaces

Mathematical Methods in the Applied Sciences, Volume 49, Issue 4, Page 3353-3384, 15 March 2026.
ABSTRACT The article examines a boundary‐value problem in a bounded domain Ωε$$ {\Omega}_{\varepsilon } $$ consisting of perforated and imperforate regions, with Neumann conditions prescribed at the boundaries of the perforations. Assuming the porous medium has symmetric, periodic structure with a small period ε$$ \varepsilon $$, we analyze the limit ...
Taras Melnyk
wiley   +1 more source

Elliptic Equations in Weighted Sobolev Spaces on Unbounded Domains

International Journal of Mathematics and Mathematical Sciences, 2008
We study in this paper a class of second-order linear elliptic equations in weighted Sobolev spaces on unbounded domains of ℝ𝑛, 𝑛≥3. We obtain an a priori bound, and a regularity result from which we deduce a uniqueness theorem.
Serena Boccia, Sara Monsurrò, Maria Transirico   +2 more
doaj   +1 more source

Carleson–Sobolev measures for weighted Bloch spaces

Journal of Functional Analysis, 2010
Let \(B_n\) denote the unit ball in \( \mathbb C^n.\) The class of all homomorphic functions on \(B_n\) will be denoted by \(H(B_n).\) Let \(f \in H(B_n)\) have the homogeneous expansion \(f(z)=\sum_{k=1}^\infty f_k(z).\) For each non-negative integer \(j\), we define \({\mathcal R}^j f(z)=\sum_{k=1}^\infty k^jf_k(z).\) For each real parameter \(\alpha\
openaire   +1 more source

Accelerating Conjugate Gradient Solvers for Homogenization Problems With Unitary Neural Operators

International Journal for Numerical Methods in Engineering, Volume 127, Issue 5, 15 March 2026.
ABSTRACT Rapid and reliable solvers for parametric partial differential equations (PDEs) are needed in many scientific and engineering disciplines. For example, there is a growing demand for composites and architected materials with heterogeneous microstructures.
Julius Herb, Felix Fritzen
wiley   +1 more source