Cauchy’s Problem for Systems of First Order Analytic Elliptic Equations in the Plan

1977 ◽  
Vol 8 (4) ◽  
pp. 719-740
Author(s):  
Chung-Ling Yu
Keyword(s):  
Elliptic Equations ◽  
First Order

Analysis of a New Mixed Finite Volume Method

2003 ◽  
Vol 3 (1) ◽  
pp. 189-201 ◽  
Author(s):  
Ilya D. Mishev
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Elliptic Equations ◽  
Variable Pressure ◽  
Order Error ◽  
First Order ◽  
Scalar Variable ◽  
Volume Method ◽  
Well Posed ◽  
Theoretical Results

AbstractA new mixed finite volume method for elliptic equations with tensor coefficients on rectangular meshes (2 and 3-D) is presented. The implementation of the discretization as a finite volume method for the scalar variable (“pressure”) is derived. The scheme is well suited for heterogeneous and anisotropic media because of the generalized harmonic averaging. It is shown that the method is stable and well posed. First-order error estimates are derived. The theoretical results are confirmed by the presented numerical experiments.

scholarly journals The Moving Plane Method for Doubly Singular Elliptic Equations Involving a First-Order Term

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Francesco Esposito ◽  
Berardino Sciunzi
Keyword(s):  
Elliptic Equations ◽  
Order Term ◽  
Singular Solutions ◽  
Moving Plane Method ◽  
Plane Method ◽  
First Order ◽  
Semilinear Elliptic ◽  
Singular Elliptic Equations ◽  
Moving Plane ◽  
Semilinear Elliptic Problems

Abstract In this paper we deal with positive singular solutions to semilinear elliptic problems involving a first-order term and a singular nonlinearity. Exploiting a fine adaptation of the well-known moving plane method of Alexandrov–Serrin and a careful choice of the cutoff functions, we deduce symmetry and monotonicity properties of the solutions.

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