Results 11 to 20 of about 99,299 (234)
Essential spectra of elliptic partial differential equations [PDF]
Bulletin of the American Mathematical Society, 1967 Let A be a closed, densely defined operator in a Banach space X. There are several definitions of the "essential" spectrum of A (cf. [ l ] , [2]). According to Wolf [3], [4] it is the complement in the complex plane of the $-set of A. The $-set $A of A is the set of points X for which (a) a(A — X), the dimension of the null space of A — X, is finite (b)
Martin Schechter
openaire +5 more sources
On the Solutions of Quasi-Linear Elliptic Partial Differential Equations [PDF]
Transactions of the American Mathematical Society, 1938 The literature concerning these equations being very extensive, we shall not attempt to give a complete list of references. The starting point for many more modern researches has been the work of S. Bernstein,t who was the first to prove the analyticity of the solutions of the general equation with 4 analytic and who was able to obtain a priori bounds ...
Charles B. Morrey
openaire +3 more sources
On Classes of Solutions of Elliptic Linear Partial Differential Equations [PDF]
Proceedings of the American Mathematical Society, 1957 Introduction. Among the theorems which deal with the functional properties of the solutions of elliptic linear partial differential equations, the most important ones are perhaps the following: (a) The solutions of equations with analytic coefficients are analytic.
Avner Friedman
openaire +4 more sources
Lectures on Elliptic Partial Differential Equations
, 2018 The volume develops several basic classical topics of the qualitative theory of elliptic partial differential equations and calculus of variations, including recent contributions to partial regularity for systems and the theory of viscosity solutions. The content is divided into the following five chapters: I.
Ambrosio, Luigi +2 more
openaire +3 more sources
An elliptic partial differential equation and its application [PDF]
Applied Mathematics Letters, 2020 This paper deals with the following elliptic equation \begin{equation*} -2 ^{2} z+\left\| \nabla z\right\| ^{2}+4 z=4\left\| x\right\| ^{2}\text{ for }x\in \mathbb{R}^{N}\text{, (}% N\geq 1\text{),} \end{equation*}% where $ >0,$ $ >0$ are some real parameters. The solution method is based on the sub- and super-solutions approach. The case $N&
Dragos-Patru Covei, Traian A. Pirvu
openaire +3 more sources
Application of decomposition to hyperbolic, parabolic, and elliptic partial differential equations
International Journal of Mathematics and Mathematical Sciences, 1989 The decomposition method is applied to examples of hyperbolic, parabolic, and elliptic partial differential equations without use of linearizatlon techniques.
G. Adomian
doaj +1 more source
Differential-Difference Elliptic Equations with Nonlocal Potentials in Half-Spaces
Mathematics, 2023 We investigate the half-space Dirichlet problem with summable boundary-value functions for an elliptic equation with an arbitrary amount of potentials undergoing translations in arbitrary directions.
Andrey B. Muravnik
doaj +1 more source
Path Integral Solution of Linear Second Order Partial Differential Equations I. The General Construction [PDF]
, 2004 A path integral is presented that solves a general class of linear second order partial differential equations with Dirichlet/Neumann boundary conditions. Elementary kernels are constructed for both Dirichlet and Neumann boundary conditions.
Abraham +16 more
core +2 more sources
Hopscotch methods for elliptic partial differential equations
Journal of Computational and Applied Mathematics, 1979 AbstractThis paper analyses hopscotch algorithms when used to solve elliptic partial differential equations. A comparison with standard methods is made for the model problem.
Sean McKee, A.R. Gourlay
openaire +3 more sources
The Extended Trial Equation Method for Some Time Fractional Differential Equations
Discrete Dynamics in Nature and Society, 2013 Nonlinear fractional partial differential equations have been solved with the help of the extended trial equation method. Based on the fractional derivative in the sense of modified Riemann-Liouville derivative and traveling wave transformation, the ...
Yusuf Pandir +2 more
doaj +1 more source