scholarly journals On Maximum Principles for -Metaharmonic Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
A. Mareno
Keyword(s):  
Partial Differential Equations ◽  
Maximum Principle ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
A Priori ◽  
Elliptic Partial Differential Equations ◽  
Maximum Principles ◽  
A Priori Bounds ◽  
Even Order ◽  
Homogeneous Linear

We study homogeneous linear elliptic partial differential equations of even order. Several maximum principle results are deduced for such equations as well as a priori bounds for certain boundary value problems.

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 AnLp-Estimate for Weak Solutions of Elliptic Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Sara Monsurrò ◽  
Maria Transirico
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Weak Solutions ◽  
Elliptic Equations ◽  
A Priori ◽  
Unbounded Domains ◽  
Discontinuous Coefficients ◽  
Elliptic Partial Differential Equations ◽  
Divergence Form ◽  
A Priori Bound

We prove anLp-a priori bound,p>2, for solutions of second order linear elliptic partial differential equations in divergence form with discontinuous coefficients in unbounded domains.

scholarly journals On the rigorous foundations of the Fokas method for linear elliptic partial differential equations

2012 ◽  
Vol 468 (2141) ◽  
pp. 1325-1331 ◽  
Author(s):  
A. C. L. Ashton
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Complex Analysis ◽  
Boundary Value ◽  
Elliptic Partial Differential Equations ◽  
Unknown Boundary ◽  
Partial Differential ◽  
Global Relation ◽  
Fokas Method

In this paper, we address some of the rigorous foundations of the Fokas method, confining attention to boundary value problems for linear elliptic partial differential equations on bounded convex domains. The central object in the method is the global relation, which is an integral equation in the spectral Fourier space that couples the given boundary data with the unknown boundary values. Using techniques from complex analysis of several variables, we prove that a solution to the global relation provides a solution to the corresponding boundary value problem, and that the solution to the global relation is unique. The result holds for any number of spatial dimensions and for a variety of boundary value problems.

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

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