scholarly journals A priori estimates in geometry and Sobolev spaces on open manifolds

1992 ◽  
Vol 27 (1) ◽  
pp. 141-146 ◽  
Author(s):  
Jürgen Eichhorn
Keyword(s):  
Sobolev Spaces ◽  
A Priori Estimates ◽  
A Priori ◽  
Open Manifolds ◽  
Priori Estimates

scholarly journals The Cauchy–Neumann and Cauchy–Robin problems for a class of hyperbolic operators with double characteristics in presence of transition

2020 ◽  
Vol 11 (4) ◽  
pp. 1991-2022
Author(s):  
Annamaria Barbagallo ◽  
Vincenzo Esposito
Keyword(s):  
Sobolev Spaces ◽  
Existence And Uniqueness ◽  
A Priori Estimates ◽  
A Priori ◽  
Existence And Uniqueness Results ◽  
Mixed Problems ◽  
Uniqueness Results ◽  
Hyperbolic Operators ◽  
Priori Estimates

Abstract The mixed Cauchy–Neumann and Cauchy–Robin problems for a class of hyperbolic operators with double characteristics in presence of transition is investigated. Some a priori estimates in Sobolev spaces with negative indexes are proved. Subsequently, existence and uniqueness results for the mixed problems are obtained.

scholarly journals On the Cauchy problem for a class of hyperbolic operators with triple characteristics

2020 ◽  
Author(s):  
Annamaria Barbagallo ◽  
Vincenzo Esposito
Keyword(s):  
Cauchy Problem ◽  
Sobolev Spaces ◽  
Existence Result ◽  
A Priori Estimates ◽  
A Priori ◽  
Hyperbolic Operators ◽  
Priori Estimates ◽  
The Cauchy Problem

AbstractThe Cauchy problem for a class of hyperbolic operators with triple characteristics is analyzed. Some a priori estimates in Sobolev spaces with negative indexes are proved. Subsequently, an existence result for the Cauchy problem is obtained.

A priori estimates in Sobolev spaces for a class of hyperbolic operators in presence of transition

2019 ◽  
Vol 16 (02) ◽  
pp. 245-270 ◽  
Author(s):  
Annamaria Barbagallo ◽  
Vincenzo Esposito
Keyword(s):  
Sobolev Spaces ◽  
A Priori Estimates ◽  
A Priori ◽  
Second Order ◽  
Hyperbolic Operators ◽  
Priori Estimates ◽  
Euclidian Space ◽  
Global Nature

We establish several a priori estimates of local or global nature in Sobolev spaces with general exponent [Formula: see text] for a class of second-order hyperbolic operators with double characteristics in presence of a transition in a domain of the Euclidian space [Formula: see text].

scholarly journals Regularity results for nonlocal evolution Venttsel’ problems

2020 ◽  
Vol 23 (5) ◽  
pp. 1416-1430 ◽  
Author(s):  
Simone Creo ◽  
Maria Rosaria Lancia ◽  
Alexander I. Nazarov
Keyword(s):  
Sobolev Spaces ◽  
Fractional Laplacian ◽  
A Priori Estimates ◽  
A Priori ◽  
Extension Theorem ◽  
Weighted Sobolev Spaces ◽  
Nonlocal Term ◽  
Two Dimensional ◽  
Priori Estimates ◽  
Regularity Results

Abstract We consider parabolic nonlocal Venttsel’ problems in polygonal and piecewise smooth two-dimensional domains and study existence, uniqueness and regularity in (anisotropic) weighted Sobolev spaces of the solution. The nonlocal term can be regarded as a regional fractional Laplacian on the boundary. The regularity results deeply rely on a priori estimates, obtained via the so-called Munchhausen trick, and sophisticated extension theorem for anisotropic weighted Sobolev spaces.

scholarly journals Elliptic Problems with Additional Unknowns in Boundary Conditions and Generalized Sobolev Spaces

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 292
Author(s):  
Anna Anop ◽  
Iryna Chepurukhina ◽  
Aleksandr Murach
Keyword(s):  
Boundary Conditions ◽  
Sobolev Spaces ◽  
Differential Operators ◽  
A Priori Estimates ◽  
A Priori ◽  
Sufficient Conditions ◽  
Inner Product ◽  
Generalized Solutions ◽  
Bounded Operators ◽  
Priori Estimates

In generalized inner product Sobolev spaces we investigate elliptic differential problems with additional unknown functions or distributions in boundary conditions. These spaces are parametrized with a function OR-varying at infinity. This characterizes the regularity of distributions more finely than the number parameter used for the Sobolev spaces. We prove that these problems induce Fredholm bounded operators on appropriate pairs of the above spaces. Investigating generalized solutions to the problems, we prove theorems on their regularity and a priori estimates in these spaces. As an application, we find new sufficient conditions under which components of these solutions have continuous classical derivatives of given orders. We assume that the orders of boundary differential operators may be equal to or greater than the order of the relevant elliptic equation.

The Dirichlet problem for the uniformly elliptic equation in generalized weighted Morrey spaces

2020 ◽  
Vol 57 (1) ◽  
pp. 68-90 ◽  
Author(s):  
Tahir S. Gadjiev ◽  
Vagif S. Guliyev ◽  
Konul G. Suleymanova
Keyword(s):  
Elliptic Equations ◽  
A Priori Estimates ◽  
A Priori ◽  
Morrey Spaces ◽  
Smooth Bounded Domain ◽  
Weighted Morrey Spaces ◽  
Priori Estimates ◽  
Muckenhoupt Class ◽  
Morrey Estimates ◽  
Dirichlet Boundary Problem

Abstract In this paper, we obtain generalized weighted Sobolev-Morrey estimates with weights from the Muckenhoupt class Ap by establishing boundedness of several important operators in harmonic analysis such as Hardy-Littlewood operators and Calderon-Zygmund singular integral operators in generalized weighted Morrey spaces. As a consequence, a priori estimates for the weak solutions Dirichlet boundary problem uniformly elliptic equations of higher order in generalized weighted Sobolev-Morrey spaces in a smooth bounded domain Ω ⊂ ℝn are obtained.

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