scholarly journals Sobolev Spaces with Non-Muckenhoupt Weights, Fractional Elliptic Operators, and Applications

2019 ◽  
Vol 51 (3) ◽  
pp. 2479-2503 ◽  
Author(s):  
Harbir Antil ◽  
Carlos N. Rautenberg
Keyword(s):  
Sobolev Spaces ◽  
Elliptic Operators ◽  
Muckenhoupt Weights

scholarly journals Pseudo-monotonicity and degenerated or singular elliptic operators

1998 ◽  
Vol 58 (2) ◽  
pp. 213-221 ◽  
Author(s):  
P. Drábek ◽  
A. Kufner ◽  
V. Mustonen
Keyword(s):  
Sobolev Spaces ◽  
Differential Operators ◽  
Weighted Sobolev Spaces ◽  
Type Inequality ◽  
Elliptic Operators ◽  
Hardy Type Inequality ◽  
Hardy Type ◽  
Elliptic Differential Operators

Using the compactness of an imbedding for weighted Sobolev spaces (that is, a Hardy-type inequality), it is shown how the assumption of monotonicity can be weakened still guaranteeing the pseudo-monotonicity of certain nonlinear degenerated or singular elliptic differential operators. The result extends analogous assertions for elliptic operators.

scholarly journals Selfadjointness of degenerate elliptic operators on higher order Sobolev spaces

2011 ◽  
Vol 4 (3) ◽  
pp. 581-593
Author(s):  
Angelo Favini ◽  
◽  
Gisèle Ruiz Goldstein ◽  
Jerome A. Goldstein ◽  
Silvia Romanelli ◽  
...  
Keyword(s):  
Sobolev Spaces ◽  
Higher Order ◽  
Elliptic Operators ◽  
Degenerate Elliptic Operators ◽  
Degenerate Elliptic

scholarly journals Pseudodifferential calculus on noncommutative tori, II. Main properties

2019 ◽  
Vol 30 (08) ◽  
pp. 1950034 ◽  
Author(s):  
Hyunsu Ha ◽  
Gihyun Lee ◽  
Raphaël Ponge
Keyword(s):  
Spectral Theory ◽  
Trace Formula ◽  
Sobolev Spaces ◽  
Pseudodifferential Operators ◽  
Elliptic Operators ◽  
Schatten Class ◽  
Noncommutative Tori ◽  
Dimension Formula ◽  
Pseudodifferential Calculus ◽  
Negative Order

This paper is the second part of a two-paper series whose aim is to give a detailed description of Connes’ pseudodifferential calculus on noncommutative [Formula: see text]-tori, [Formula: see text]. We make use of the tools introduced in the 1st part to deal with the main properties of pseudodifferential operators on noncommutative tori of any dimension [Formula: see text]. This includes the main results mentioned in [2, 5, 11]. We also obtain further results regarding action on Sobolev spaces, spectral theory of elliptic operators, and Schatten-class properties of pseudodifferential operators of negative order, including a trace-formula for pseudodifferential operators of order [Formula: see text].

scholarly journals Kolmogorov and Linear Widths of Balls in Sobolev Spaces on Compact Manifolds

2014 ◽  
Vol 115 (1) ◽  
pp. 96 ◽  
Author(s):  
Daryl Geller ◽  
Isaac Z. Pesenson
Keyword(s):  
Sobolev Spaces ◽  
Riemannian Manifolds ◽  
Elliptic Operators ◽  
Compact Manifolds ◽  
Asymptotic Estimates ◽  
Homogeneous Manifolds ◽  
Uniform Estimates ◽  
Cubature Formulas ◽  
Sobolev Norms ◽  
Positive Coefficients

We determine upper asymptotic estimates of Kolmogorov and linear $n$-widths of unit balls in Sobolev norms in $L_{p}$-spaces on smooth compact Riemannian manifolds. For compact homogeneous manifolds, we establish estimates which are asymptotically exact, for the natural ranges of indices. The proofs heavily rely on our previous results such as: estimates for the near-diagonal localization of the kernels of elliptic operators, Plancherel-Polya inequalities on manifolds, cubature formulas with positive coefficients and uniform estimates on Clebsch-Gordon coefficients on general compact homogeneous manifolds.

scholarly journals A Priori Bounds for a Class of Elliptic Operators

2011 ◽  
Vol 2011 ◽  
pp. 1-17 ◽  
Author(s):  
Sara Monsurrò ◽  
Maria Salvato ◽  
Maria Transirico
Keyword(s):  
Dirichlet Problem ◽  
Existence Theorem ◽  
Sobolev Spaces ◽  
Differential Operators ◽  
A Priori ◽  
Weighted Sobolev Spaces ◽  
Unbounded Domains ◽  
Elliptic Operators ◽  
A Priori Bounds ◽  
Uniqueness And Existence

We obtain some a priori bounds for a class of uniformly elliptic second-order differential operators, both in a no-weighted and in a weighted case. We deduce a uniqueness and existence theorem for the related Dirichlet problem in some weighted Sobolev spaces on unbounded domains.

Sobolev Spaces with Muckenhoupt Weights, Singularities and Inequalities

2008 ◽  
Vol 15 (2) ◽  
pp. 263-280
Author(s):  
Dorothee D. Haroske
Keyword(s):  
Sobolev Spaces ◽  
Weighted Spaces ◽  
Muckenhoupt Weights ◽  
Growth Envelopes

Abstract We use the recently introduced concept of growth envelopes to characterize weighted spaces of type , where 𝑤 belongs to some Muckenhoupt 𝐴𝑝 class, and discuss some applications.

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