scholarly journals Uniqueness Results through a Priori Estimates Part II. Dirichlet Problem

2000 ◽  
Vol 248 (1) ◽  
pp. 156-172 ◽  
Author(s):  
Meijun Zhu
Keyword(s):  
Dirichlet Problem ◽  
A Priori Estimates ◽  
A Priori ◽  
Uniqueness Results ◽  
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 nonlocal minimal graphs

2021 ◽  
Vol 60 (4) ◽  
Author(s):  
Matteo Cozzi ◽  
Luca Lombardini
Keyword(s):  
Existence And Uniqueness ◽  
A Priori Estimates ◽  
A Priori ◽  
Analytic Approach ◽  
Comparison Principles ◽  
Minimal Graphs ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Priori Estimates ◽  
Rearrangement Inequalities

AbstractWe develop a functional analytic approach for the study of nonlocal minimal graphs. Through this, we establish existence and uniqueness results, a priori estimates, comparison principles, rearrangement inequalities, and the equivalence of several notions of minimizers and solutions.

scholarly journals Weighted Pluricomplex Energy II

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Slimane Benelkourchi
Keyword(s):  
Dirichlet Problem ◽  
Orlicz Space ◽  
Boundary Data ◽  
Borel Measure ◽  
A Priori Estimates ◽  
A Priori ◽  
Unique Function ◽  
A Priori Bounds ◽  
Priori Estimates ◽  
Monge Ampere

We continue our study of the complex Monge-Ampère operator on the weighted pluricomplex energy classes. We give more characterizations of the range of the classes Eχ by the complex Monge-Ampère operator. In particular, we prove that a nonnegative Borel measure μ is the Monge-Ampère of a unique function φ∈Eχ if and only if χ(Eχ)⊂L1(dμ). Then we show that if μ=(ddcφ)n for some φ∈Eχ then μ=(ddcu)n for some φ∈Eχ, where f is given boundary data. If moreover the nonnegative Borel measure μ is suitably dominated by the Monge-Ampère capacity, we establish a priori estimates on the capacity of sublevel sets of the solutions. As a consequence, we give a priori bounds of the solution of the Dirichlet problem in the case when the measure has a density in some Orlicz space.

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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