A priori estimates for solutions of elliptic partial differential equations on surfaces

2009 ◽  
Author(s):  
Heidi Steenblock
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
A Priori Estimates ◽  
A Priori ◽  
Elliptic Partial Differential Equations ◽  
Partial Differential ◽  
Priori Estimates

Higher-order estimates for fully nonlinear difference equations. I

2000 ◽  
Vol 43 (3) ◽  
pp. 485-510 ◽  
Author(s):  
Derek W. Holtby
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Difference Equations ◽  
A Priori ◽  
Elliptic Partial Differential Equations ◽  
Uniform Mesh ◽  
Partial Differential ◽  
Fully Nonlinear ◽  
Nonlinear Elliptic ◽  
Special Case

AbstractThe purpose of this work is to establish a priori C2, α estimates for mesh function solutions of nonlinear positive difference equations in fully nonlinear form on a uniform mesh, where the fully nonlinear finite-difference operator ℱh is concave in the second-order variables. The estimate is an analogue of the corresponding estimate for solutions of concave fully nonlinear elliptic partial differential equations. We deal here with the special case that the operator does not depend explicitly upon the independent variables. We do this by discretizing the approach of Evans for fully nonlinear elliptic partial differential equations using the discrete linear theory of Kuo and Trudinger. The result in this special case forms the basis for a more general result in part II. We also derive the discrete interpolation inequalities needed to obtain estimates for the interior C2, α semi-norm in terms of the C0 norm.

scholarly journals Existence of Positive Solution for a Nonlinear Weighted Bi-Harmonic System of Elliptic Partial Differential Equations via Fixed-Point Argument

2020 ◽  
Vol 40 (1) ◽  
pp. 54-70
Author(s):  
Md Asaduzzamana ◽  
Md Zulfikar Ali
Keyword(s):  
Fixed Point ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Positive Solution ◽  
A Priori ◽  
Elliptic Partial Differential Equations ◽  
Partial Differential ◽  
Existence Criterion ◽  
Point Argument ◽  
Harmonic System

In this paper, we establish an existence criterion of positive solution for a nonlinear weighted bi-harmonic system of elliptic partial differential equations in the unit ball in Nn ( dimensionaleuclideanspace) The analysis of this paper is based on a topological method (a fixed-point argument). Initially, we establish a priori solution estimates, and then use a fixed-point theorem for deducing the existence of positive solutions. Finally, we prove a non-existence criterion as the complement of existence criterion. GANIT J. Bangladesh Math. Soc.Vol. 40 (2020) 54-70

scholarly journals A priori bounds of the solution of a one point IBVP for a singular fractional evolution equation

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Said Mesloub ◽  
Hassan Eltayeb Gadain
Keyword(s):  
Differential Equations ◽  
Evolution Equation ◽  
A Priori Estimates ◽  
Boundary Value ◽  
A Priori ◽  
Initial Boundary ◽  
A Priori Bounds ◽  
Fractional Evolution Equation ◽  
Priori Estimates ◽  
Initial Boundary Value

Abstract A priori bounds constitute a crucial and powerful tool in the investigation of initial boundary value problems for linear and nonlinear fractional and integer order differential equations in bounded domains. We present herein a collection of a priori estimates of the solution for an initial boundary value problem for a singular fractional evolution equation (generalized time-fractional wave equation) with mass absorption. The Riemann–Liouville derivative is employed. Results of uniqueness and dependence of the solution upon the data were obtained in two cases, the damped and the undamped case. The uniqueness and continuous dependence (stability of solution) of the solution follows from the obtained a priori estimates in fractional Sobolev spaces. These spaces give what are called weak solutions to our partial differential equations (they are based on the notion of the weak derivatives). The method of energy inequalities is used to obtain different a priori estimates.

Sign in / Sign up

Export Citation Format

Share Document