Results 41 to 50 of about 27,220 (202)

Weierstrass' Theorem in Weighted Sobolev Spaces

Journal of Approximation Theory, 2001
It is very well known that given any compact interval \(I\), the set of all continuous (almost everywhere) functions \(C(I)\) on \(I\) is the biggest set of functions that can be approximated by polynomials in the \(L^\infty(I)\) norm. This result is the very classical Weierstrass' Theorem. There are many generalizations of this result [see e.g.
openaire   +2 more sources

Advanced control of non‐isothermal axial dispersion tubular reactors with recycle‐induced state delay

The Canadian Journal of Chemical Engineering, EarlyView.
Abstract We develop a delay‐aware estimation and control framework for a non‐isothermal axial dispersion tubular reactor modelled as a coupled parabolic‐hyperbolic PDE system with recycle‐induced state delay. The infinite‐dimensional dynamics are preserved without spatial discretization by representing the delay as a transport PDE and adopting a late ...
Behrad Moadeli, Stevan Dubljevic
wiley   +1 more source

Shape Derivatives of the Eigenvalues of the De Rham Complex for Lipschitz Deformations and Variable Coefficients: Part I

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT We study eigenvalue problems for the de Rham complex on varying three‐dimensional domains. Our analysis includes the Helmholtz equation as well as the Maxwell system with mixed boundary conditions and non‐constant coefficients. We provide Hadamard‐type formulas for the shape derivatives under weak regularity assumptions on the domain and its ...
Pier Domenico Lamberti, Dirk Pauly, Michele Zaccaron   +2 more
wiley   +1 more source

𝑊𝟐,𝟐 A Priori Bounds for a Class of Elliptic Operators

International Journal of Differential Equations, 2011
We obtain some 𝑊2,2 a priori bounds for a class of uniformly elliptic second-order differential operators, both in a no-weighted and in a weighted case.
Sara Monsurrò, Maria Salvato, Maria Transirico   +2 more
doaj   +1 more source

Asymptotics for the Spectrum of the Laplacian in Thin Bars with Varying Cross Sections

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT We consider spectral problems for the Laplace operator in 3D rod structures with a small cross section of diameter O(ε)$$ O\left(\varepsilon \right) $$, ε$$ \varepsilon $$ being a positive parameter. The boundary conditions are Dirichlet (Neumann, respectively) on the bases of this structure, and Neumann on the lateral boundary.
Pablo Benavent‐Ocejo, Delfina Gómez, Maria‐Eugenia Pérez‐Martínez   +2 more
wiley   +1 more source

Weak Solutions for a Class of Nonlocal Singular Problems Over the Nehari Manifold

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT In this paper, we consider a nonlocal model of dilatant non‐Newtonian fluid with a Dirichlet boundary condition. By using the Nehari manifold and fibering map methods, we obtain the existence of at least two weak solutions, with sign information.
Zhenfeng Zhang, Calogero Vetro, Tianqing An   +2 more
wiley   +1 more source

Sobolev meets Riesz: a characterization of weighted Sobolev spaces via weighted Riesz bounded variation space

, 2023
We introduce weighted Riesz bounded variation spaces defined on an open subset of the $n$-dimensional Euclidean space and use them to characterize weighted Sobolev spaces when the weight belongs to the Muckenhoupt class. As an application, using Rubio de Francia's extrapolation theory, a similar characterization of the variable exponent Sobolev spaces ...
Cruz-Uribe, David, Guzman, Oscar, Rafeiro, Humberro   +2 more
openaire   +2 more sources

Phase‐Pole‐Free Images and Smooth Coil Sensitivity Maps by Regularized Nonlinear Inversion

Magnetic Resonance in Medicine, EarlyView.
ABSTRACT Purpose Phase singularities are a common problem in image reconstruction with auto‐calibrated sensitivities due to an inherent ambiguity of the estimation problem. The purpose of this work is to develop a method for detecting and correcting phase poles in non‐linear inverse (NLINV) reconstruction of MR images and coil sensitivity maps ...
Moritz Blumenthal, Martin Uecker
wiley   +1 more source

Lq-differentials for weighted Sobolev spaces.

Michigan Mathematical Journal, 2000
The author generalizes the well known theorem (Calderón, Zygmund) about \(L^q\)-differentials of Sobolev functions to functions from weighted Sobolev spaces.
openaire   +2 more sources

Computing Skinning Weights via Convex Duality

Computer Graphics Forum, EarlyView.
We present an alternate optimization method to compute bounded biharmonic skinning weights. Our method relies on a dual formulation, which can be optimized with a nonnegative linear least squares setup. Abstract We study the problem of optimising for skinning weights through the lens of convex duality.
J. Solomon, O. Stein
wiley   +1 more source