Results 41 to 50 of about 27,468 (197)
Covariant Poisson equation with compact Lie algebras
, 2002 The covariant Poisson equation for Lie algebra-valued mappings defined in 3-dimensional Euclidean space is studied using functional analytic methods. Weighted covariant Sobolev spaces are defined and used to derive sufficient conditions for the existence
Aubin T. +6 more
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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
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
G-Expectation Weighted Sobolev Spaces, Backward SDE and Path Dependent PDE [PDF]
, 2014 We introduce a new notion of G-expectation-weighted Sobolev spaces, or in short, G-Sobolev spaces, and prove that a backward SDEs driven by G-Brownian motion are in fact path dependent PDEs in the corresponding Sobolev spaces under G-norms.
Peng, Shige, Song, Yongsheng
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Stability of Viscous Three‐Dimensional Stratified Couette Flow via Dispersion and Mixing
Communications on Pure and Applied Mathematics, EarlyView.ABSTRACT This article explores the stability of stratified Couette flow in the viscous 3d$3d$ Boussinesq equations. In this system, mixing effects arise from the shearing background, and gravity acts as a restoring force leading to dispersive internal gravity waves.
Michele Coti Zelati +2 more
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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 +2 more
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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 +2 more
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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 +2 more
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, 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 +2 more
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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 +2 more
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