scholarly journals The augmented operator of a surjective partial differential operator with constant coefficients need not be surjective

2011 ◽  
Vol 44 (3) ◽  
pp. 610-614 ◽  
Author(s):  
T. Kalmes
Keyword(s):  
Differential Operator ◽  
Partial Differential Operator ◽  
Partial Differential ◽  
Constant Coefficients

scholarly journals Some Spaces are not the Domain of a Closed Linear Operator in a Banach Space

1980 ◽  
Vol 23 (4) ◽  
pp. 501-503
Author(s):  
Peter Dierolf ◽  
Susanne Dierolf
Keyword(s):  
Banach Space ◽  
Differential Operator ◽  
Linear Operator ◽  
Partial Differential Operator ◽  
Linear Partial Differential Operator ◽  
Closed Linear Operator ◽  
Partial Differential ◽  
Minimal Operator ◽  
Constant Coefficients

Let be a linear partial differential operator with C∞- coefficients. The study of P(∂) as an operator in L2(ℝn) usually starts with the investigation of the minimal operator P0 which is the closure of P(∂) acting on . In the case of constant coefficients it is known that the domain D(P0) of P0 at least contains the space (cf. Schechter [4, p. 58, Lemma 1.2]).

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)

scholarly journals Wave Front Sets with respect to the Iterates of an Operator with Constant Coefficients

2014 ◽  
Vol 2014 ◽  
pp. 1-17 ◽  
Author(s):  
C. Boiti ◽  
D. Jornet ◽  
J. Juan-Huguet
Keyword(s):  
Differential Operator ◽  
Wave Front ◽  
Partial Differential Operator ◽  
Regularity Theorem ◽  
Wave Front Set ◽  
Open Set ◽  
Wave Front Sets ◽  
Constant Coefficients ◽  
New Type ◽  
Classical Distribution

We introduce the wave front setWF*P(u)with respect to the iterates of a hypoelliptic linear partial differential operator with constant coefficients of a classical distributionu∈𝒟′(Ω)in an open set Ω in the setting of ultradifferentiable classes of Braun, Meise, and Taylor. We state a version of the microlocal regularity theorem of Hörmander for this new type of wave front set and give some examples and applications of the former result.

scholarly journals On some stochastic parabolic differential equations in a Hilbert space

2005 ◽  
Vol 2005 (2) ◽  
pp. 167-173 ◽  
Author(s):  
Khairia El-Said El-Nadi
Keyword(s):  
Hilbert Space ◽  
Partial Differential Equations ◽  
Differential Operator ◽  
Differential Equations ◽  
Partial Differential Operator ◽  
Parabolic Differential Equations ◽  
Partial Differential ◽  
Mixed Problems ◽  
Uniqueness Of The Solution ◽  
Weiner Process

We consider some stochastic difference partial differential equations of the form du(x,t,c)=L(x,t,D)u(x,t,c)dt+M(x,t,D)u(x,t−a,c)dw(t), where L(x,t,D) is a linear uniformly elliptic partial differential operator of the second order, M(x,t,D) is a linear partial differential operator of the first order, and w(t) is a Weiner process. The existence and uniqueness of the solution of suitable mixed problems are studied for the considered equation. Some properties are also studied. A more general stochastic problem is considered in a Hilbert space and the results concerning stochastic partial differential equations are obtained as applications.

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