共查询到20条相似文献,搜索用时 31 毫秒
1.
Gerson Petronilho 《Indagationes Mathematicae》2005,16(1):67-90
In this paper we consider the problem of global Gevrey solvability for a class of sublaplacians on a toruswith coefficients in the Gevrey class Gs(TN). For this class of operators we show that global Gevrey solvability and global Gevrey hypoellipticity are both equivalent to the condition that the coefficients satisfy a Diophantine condition. 相似文献
2.
Gerson Petronilho 《Journal of Differential Equations》2002,184(1):48-61
We consider a class of sum of squares operators on a torus and we prove that global solvability is equivalent to an algebraic condition involving simultaneously approximable vectors. 相似文献
3.
Müller Detlef 《偏微分方程通讯》2013,38(1-2):305-337
We study questions of solvability for operators of the form p(x,D)+b, where p(x,ξ) is a real quadratic form and b?C. As one consequence, we obtain a necessary and sufficient condition for the local solvability of operators of the form L= near the critical point x=0, and prove the existence of tempered fundamental solutions whenever L is locally solvable.Our analysis of these operators is largely based on recent results about the solvabilitiy of left–invariant second order differential operators on the Heisenberg group and a transference principle for the Schrödinger representation. 相似文献
4.
Abstract In this paper we consider the problem of global analytic and Gevrey hypoellipticity and solvability for a class of partial
differential operators on a torus. We prove that global analytic and Gevrey hypoellipticity and solvability on the torus is
equivalent to certain Diophantine approximation properties.
Keywords: Global hypoellipticity, Global solvability, Gevrey classes, Diophantine approximation property
Mathematics Subject Classification (2000): 35D05, 46E10, 46F05, 58J99 相似文献
5.
We consider a class of degenerate elliptic operators on a torus and prove that global hypoellipticity is equivalent to an
algebraic condition involving Liouville vectors and simultaneous approximability. For another class of operators we show that
the zero order term may influence global hypoellipticity.
Received August 13, 1997 相似文献
6.
E. I. Bravyi 《Russian Mathematics (Iz VUZ)》2011,55(10):13-22
We consider first-order systems of linear functional differential equations with regular operators. For families of systems
of two equations we obtain the general necessary and sufficient conditions for the unique solvability of a periodic boundary-value
problem. For families of systems of n linear functional differential equations with cyclic matrices we obtain effective necessary and sufficient conditions for
the unique solvability of a periodic boundary-value problem. 相似文献
7.
V. A. Nikishkin 《Differential Equations》2011,47(3):446-450
We consider boundary value problems for elliptic operators with constant coefficients in a layer, i.e., in a domain between
two parallel planes. We assume that the Lopatinskii condition and the condition of the unique solvability of an auxiliary
problem for an ordinary differential operator are satisfied. We prove theorems on the solvability and smoothness of solutions
in Sobolev spaces with weight of exponential type. 相似文献
8.
In this paper we consider the problem of global analytic and Gevrey solvability for a class of partial differential operators
on a torus in the form of squares of vector fields. We prove that global analytic and Gevrey solvability on the torus is equivalent
to certain Diophantine approximation properties.
Mathematics Subject Classification (2000) 35D05, 46E10, 46F05, 58J99 相似文献
9.
The paper is devoted to general linear elliptic problems in Hölder spaces. We consider unbounded domains and define limiting problems at infinity. We give a necessary and sufficient condition of normal solvability through uniqueness of solutions of limiting problems. We study a structure of spaces dual to Hölder spaces and specify the subspace of functionals, which provide the condition of normal solvability. This allows us to prove that for Fredholm operators all limiting operators are invertible. To cite this article: V. Volpert, A. Volpert, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 457–462. 相似文献
10.
A. V. Tarasenko 《Russian Mathematics (Iz VUZ)》2013,57(1):64-71
For a mixed-type equation we study a problem with generalized fractional integrodifferentiation operators in the boundary condition. We prove its unique solvability under inequality-type conditions imposed on the known functions for various orders of fractional integrodifferentiation operators. We prove the existence of a solution to the problem by reducing the latter to a fractional differential equation. 相似文献
11.
We consider initial-value problems for a new class of systems of equations that combine the structures of Solonnikov parabolic
systems and Eidel’man parabolic systems. We prove a theorem on the correct solvability of these problems in H?lder spaces
of rapidly increasing functions and obtain an estimate for the norms of solutions via the corresponding norms of the right-hand
sides of the problem. For the correctness of this estimate, the condition of the parabolicity of the system is not only sufficient
but also necessary. 相似文献
12.
Farrukh Mukhamedov Otabek Khakimov Ahmad Fadillah Embong 《Mathematical Methods in the Applied Sciences》2020,43(15):9102-9118
In the present paper, we consider integral equations, which are associated with nonlinear Markov operators acting on an infinite-dimensional space. The solvability of these equations is examined by investigating nonlinear Markov operators. Notions of orthogonal preserving and surjective nonlinear Markov operators defined on infinite dimension are introduced, and their relations are studied, which will be used to prove the main results. We show that orthogonal preserving nonlinear Markov operators are not necessarily satisfied surjective property (unlike finite case). Thus, sufficient conditions for the operators to be surjective are described. Using these notions and results, we prove the solvability of Hammerstein equations in terms of surjective nonlinear Markov operators. 相似文献
13.
We establish well-posed solvability of the Cauchy problem for the Shilov parabolic equations with time-dependent coefficients whose initial data are tempered distributions. For a certain class of equations we state necessary and sufficient conditions for unique solvability of the Cauchy problem whose properties with respect to the spatial variable are typical for a fundamental solution. The results are characterized only by the order and the parabolicity exponent. 相似文献
14.
This work is devoted to the solvability and finite time blow-up of solutions of the Cauchy problem for the dissipative Boussinesq equation in all space dimension. We prove the existence and uniqueness of local mild solutions in the phase space by means of the contraction mapping principle. By establishing the time-space estimates of the corresponding Green operators, we obtain the continuation principle. Under some restriction on the initial data, we further study the results on existence and uniqueness of global solutions and finite time blow-up of solutions with the initial energy at three different level. Moreover, the sufficient and necessary conditions of finite time blow-up of solutions are given. 相似文献
15.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1999,328(10):859-864
Our aim is to study the oblique derivative problem for a class of nonlinear differential operators in the plane with quadratic growth. We assume the discontinuous operators to satisfy Carathéodory's condition and a suitable ellipticity condition. Under some geometrical conditions we prove strong solvability of the problem under consideration. The main tool in the proof is Leray-Schauder fixed point theorem, that reduces the solvability of the problem to the establishment of a priori estimate, by means of a step by step procedure. 相似文献
16.
G. V. Demidenko 《Siberian Mathematical Journal》2008,49(5):842-851
We consider a class of matrix quasielliptic operators on the n-dimensional space. For these operators, we establish the isomorphism properties in some special scales of weighted Sobolev spaces. Basing on these properties, we prove the unique solvability of the initial value problem for a class of Sobolev type equations. 相似文献
17.
S. A. Buterin 《Differential Equations》2010,46(1):150-154
We consider the sum of the Sturm-Liouville operator and a convolution operator. We study the inverse problem of reconstructing
the convolution operator from the spectrum. This problem is reduced to a nonlinear integral equation with a singularity. We
prove the global solvability of this nonlinear equation, which permits one to show that the asymptotics of the spectrum is
a necessary and sufficient condition for the solvability of the inverse problem. The proof is constructive. 相似文献
18.
O. Y. Gryshchenko 《Journal of Mathematical Sciences》2000,102(1):3742-3748
For a nonlinear transport model, we propose a simple and economical two-step algorithm that decreases the dimension of the
system of nonlinear equations, as compared with implicit difference schemes. We prove theorems on necessary conditions for
stability with respect to the initial data for the nonlinear problem and theorems on sufficient conditions for stability in
the case of the linearized model. We also obtain theorems on approximation of the integral conservation law on a grid. The
necessary condition obtained is a condition on the coefficients of the differential equation (which singles out an admissible
class of equations) but not a condition on the ratio of the grid steps. Bibliography: 3 titles.
Translated fromObchyslyuval'na ta Prykladna Matematyka, No. 81, 1997, pp. 25–32. 相似文献
19.
Let p be an analytic polynomial on the unit disk. We obtain a necessary and sufficient condition for Toeplitz operators with the symbol z + p to be invertible on the Bergman space when all coefficients of p are real numbers. Furthermore, we establish several necessary and sufficient, easy-to-check conditions for Toeplitz operators with the symbol z + p to be invertible on the Bergman space when some coefficients of p are complex numbers. 相似文献
20.
《Mathematische Nachrichten》2018,291(5-6):729-758
We are interested in the following question: when regularity properties of a linear differential operator imply solvability of its transpose in the sense of Gevrey ultradistributions? This question is studied for a class of abstract operators that contains the usual differential operators with real‐analytic coefficients. We obtain a new proof of a global result on compact manifolds (global Gevrey hypoellipticity implying global solvability of the transpose), as well as some results in the non‐compact case by means of the so‐called property of non‐confinement of singularities. We provide applications to Hörmander operators, to operators of constant strength and to locally integrable systems of vector fields. We also analyze a conjecture stated in a recent paper of Malaspina and Nicola, which asserts that, in differential complexes naturally arising from locally integrable structures, local solvability in the sense of ultradistributions implies local solvability in the sense of distributions. We establish the validity of the conjecture when the cotangent structure bundle is spanned by the differential of a single first integral. 相似文献