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 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.

A difference scheme for equations of ocean dynamics on unstructured grids

2014 ◽  
Vol 29 (3) ◽  
Author(s):  
Alexey V. Drutsa
Keyword(s):  
Difference Scheme ◽  
Existence And Uniqueness ◽  
Large Scale ◽  
A Priori Estimates ◽  
Unstructured Grids ◽  
A Priori ◽  
Ocean Dynamics ◽  
Priori Estimates ◽  
Uniqueness Of The Solution ◽  
Grid Operators

AbstractA difference scheme on unstructured grids is constructed for the system of equations of large scale ocean dynamics. The properties of the grid problem and grid operators are studied, in particular, a series of a priori estimates and the theorem on existence and uniqueness of the solution are proved.

On Approximations to Solutions of Nonlinear Integral Equations of the Urysohn Type

1973 ◽  
Vol 16 (1) ◽  
pp. 137-141
Author(s):  
K. A. Zischka
Keyword(s):  
Existence And Uniqueness ◽  
A Priori Estimates ◽  
A Priori ◽  
Sufficient Conditions ◽  
Successive Approximations ◽  
Uniqueness Of Solutions ◽  
Nonlinear Integral Equations ◽  
Priori Estimates ◽  
The Given ◽  
Uniqueness Of A Solution

This note will derive a priori estimates of the errors due to replacing the given integral operator A by a similar operator A* of the same type when successive approximations are applied to the integral equation φ=Aφ.The existence and uniqueness of solutions to this equation follow easily by applying a well known fixed point theorem in a Banach space to the above mapping [1, 2]. Moreover, sufficient conditions for the existence and uniqueness of a solution to Urysohn's equation are stated explicitly in a note by the author [3].

ASYMPTOTIC BEHAVIOR OF STOCHASTIC DISSIPATIVE QUANTUM ZAKHAROV EQUATIONS

2013 ◽  
Vol 13 (02) ◽  
pp. 1250016 ◽  
Author(s):  
YANFENG GUO ◽  
BOLING GUO ◽  
DONGLONG LI
Keyword(s):  
Asymptotic Behavior ◽  
White Noise ◽  
Approximation Method ◽  
Existence And Uniqueness ◽  
A Priori Estimates ◽  
A Priori ◽  
Galerkin Approximation ◽  
Uniqueness Of Solutions ◽  
Asymptotic Behaviors ◽  
Priori Estimates

The stochastic dissipative quantum Zakharov equations with white noise are studied. The existence and uniqueness of solutions are obtained by using the standard Galerkin approximation method on the basis of the time uniform a priori estimates in various spaces. Moreover, the asymptotic behaviors of the solutions for the stochastic dissipative quantum Zakharov equations with white noise are also investigated.

scholarly journals A Result on the Existence and Uniqueness of Stationary Solutions for a Bioconvective Flow Model

2018 ◽  
Vol 2018 ◽  
pp. 1-5
Author(s):  
Aníbal Coronel ◽  
Luis Friz ◽  
Ian Hess ◽  
Alex Tello
Keyword(s):  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Flow Model ◽  
A Priori Estimates ◽  
Boundary Value ◽  
A Priori ◽  
Stationary Solutions ◽  
Local Concentration ◽  
Priori Estimates ◽  
Bioconvective Flow

In this note, we prove the existence and uniqueness of weak solutions for the boundary value problem modelling the stationary case of the bioconvective flow problem. The bioconvective model is a boundary value problem for a system of four equations: the nonlinear Stokes equation, the incompressibility equation, and two transport equations. The unknowns of the model are the velocity of the fluid, the pressure of the fluid, the local concentration of microorganisms, and the oxygen concentration. We derive some appropriate a priori estimates for the weak solution, which implies the existence, by application of Gossez theorem, and the uniqueness by standard methodology of comparison of two arbitrary solutions.

Existence and Uniqueness of Weak Solution for a Class of Elliptic Reaction-Diffusion Systems

2008 ◽  
Vol 15 (4) ◽  
pp. 619-625
Author(s):  
Abdelfatah Bouziani ◽  
Ilham Mounir
Keyword(s):  
Weak Solution ◽  
Existence And Uniqueness ◽  
Iterative Process ◽  
A Priori Estimates ◽  
A Priori ◽  
Reaction Diffusion ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Priori Estimates ◽  
Quasilinear Elliptic

Abstract We present a simple proof of the existence and uniqueness of a weak solution for a class of quasilinear elliptic reaction-diffusion systems. The proof is based on an iterative process and on some a priori estimates.

scholarly journals Lp-SOLUTIONS OF BACKWARD DOUBLY STOCHASTIC DIFFERENTIAL EQUATIONS

2012 ◽  
Vol 12 (03) ◽  
pp. 1150025 ◽  
Author(s):  
AUGUSTE AMAN
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Existence And Uniqueness ◽  
A Priori Estimates ◽  
A Priori ◽  
Stochastic Calculus ◽  
Technical Aspects ◽  
Doubly Stochastic ◽  
Priori Estimates ◽  
Lp Solutions

The goal of this paper is to solve backward doubly stochastic differential equations (BDSDEs, in short) under weak assumptions on the data. The first part is devoted to the development of some new technical aspects of stochastic calculus related to this BDSDEs. Then we derive a priori estimates and prove the existence and uniqueness of solution in Lp, p ∈ (1, 2), extending the work of Pardoux and Peng (see [12]).

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