scholarly journals Fundamental solution of partial differential operator of Schrödinger's type, III

1978 ◽  
Vol 54 (3) ◽  
pp. 62-66 ◽  
Author(s):  
Daisuke Fujiwara
Keyword(s):  
Differential Operator ◽  
Fundamental Solution ◽  
Partial Differential Operator ◽  
Partial Differential ◽  
Type Iii

A Fundamental Solution for a Nonelliptic Partial Differential Operator

1979 ◽  
Vol 31 (5) ◽  
pp. 1107-1120 ◽  
Author(s):  
Peter C. Greiner
Keyword(s):  
Vector Field ◽  
Differential Operator ◽  
Fundamental Solution ◽  
Half Plane ◽  
Partial Differential Operator ◽  
Holomorphic Vector Field ◽  
Partial Differential ◽  
Upper Half Plane ◽  
Cauchy Riemann ◽  
Image Position

Let(1)and set(2)Here . Z is the “unique” (modulo multiplication by nonzero functions) holomorphic vector-field which is tangent to the boundary of the “degenerate generalized upper half-plane”(3)In our terminology t = Re z1. We note that ℒ is nowhere elliptic. To put it into context, ℒ is of the type □b, i.e. operators like ℒ occur in the study of the boundary Cauchy-Riemann complex. For more information concerning this connection the reader should consult [1] and [2].

scholarly journals A Fundamental Solution of N. Zeilon's Operator

2000 ◽  
Vol 86 (2) ◽  
pp. 273 ◽  
Author(s):  
Peter Wagner
Keyword(s):  
Differential Operator ◽  
Fundamental Solution ◽  
Partial Differential Operator ◽  
Elliptic Integrals ◽  
Partial Differential

In this paper, we resume earlier work of N. Zeilon and of J. Fehrman and derive an explicit re- presentation by elliptic integrals of a fundamental solution of the partial differential operator $\partial_1^3+\partial_2^3+\partial_3^3$.

scholarly journals Codomains for the Cauchy-Riemann and Laplace operators inℝ2

2008 ◽  
Vol 6 (1) ◽  
pp. 71-87
Author(s):  
Lloyd Edgar S. Moyo
Keyword(s):  
Differential Operator ◽  
Fundamental Solution ◽  
Laplace Operator ◽  
Constant Coefficient ◽  
Partial Differential Operator ◽  
Linear Partial Differential Operator ◽  
Partial Differential ◽  
Nonzero Constant ◽  
Space Of Distributions ◽  
Cauchy Riemann

A codomain for a nonzero constant-coefficient linear partial differential operatorP(∂)with fundamental solutionEis a space of distributionsTfor which it is possible to define the convolutionE*Tand thus solving the equationP(∂)S=T. We identify codomains for the Cauchy-Riemann operator inℝ2and Laplace operator inℝ2. The convolution is understood in the sense of theS′-convolution.

Estimates for a beam-like partial differential operator and applications

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Meriem Belahdji ◽  
Setti Ayad ◽  
Mohammed Hichem Mortad
Keyword(s):  
Differential Operator ◽  
A Priori Estimates ◽  
A Priori ◽  
Partial Differential Operator ◽  
Partial Differential ◽  
Priori Estimates

Abstract The aim of this paper is to provide some a priori estimates for a beam-like operator. Some applications and counterexamples are also given.

scholarly journals A Construction of asymptotic solutions and the existence of smooth null-solutions for a class of non-Fuchsian partial differential operators

1997 ◽  
Vol 145 ◽  
pp. 125-142
Author(s):  
Takeshi Mandai
Keyword(s):  
Differential Operator ◽  
Differential Operators ◽  
Partial Differential Operator ◽  
Negative Integer ◽  
Asymptotic Solutions ◽  
Partial Differential ◽  
Partial Differential Operators ◽  
Real Analytic

Consider a partial differential operator(1.1) where K is a non-negative integer and aj,a are real-analytic in a neighborhood of (0, 0)

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