1,721,012 research outputs found
L^p-regularity for a class of pseudodifferential operators in R^n
No full textWe study here a class of pseudodifferential operators with weighted symbols of Shubin type. First, we develop the basic elements of the pseudodifferential calculus for these operators, proving in particular a result of L^p -boundedness. Then we
derive regularity results in the frame of suitably defined functional spaces of Sobolev type
A stability result concerning the Shannon entropy
No full textWe are concerned with a well-known characterization of the Shannon entropy by Faddeev, suitably re-examined in the frame of Ulam-Hyers "stability" of functional equations. By use of some results about number theoretical functions, we give a sufficient condition that the solutions of a suitable system of countably many functional inequalities approximate the Shannon entropy uniformly
Hypoellipticity and local solvability of pseudolocal continuous linear operators in Gevrey classes
Full text linkIn this paper we extend a well-known result concerning hypoellipticity and local solvability of linear
partial differential operators on Schwartz distributions to the framework of pseudolocal continuous linear maps T acting on Gevrey classes. Namely we prove that the Gevrey hypoellipticity of T implies the Gevrey local solvability of the transposed operator. As an application, we identify some classes of non-Gevrey-hypoelliptic operators. A fundamental kernel is also constructed for any Gevrey hypoelliptic partial differential operator
A result of L^2-well posedness concerning the system of linear elasticity in 2D
No full textWe give an L^2-well posedness result concerning an initial boundary value problem for the system of linear elasticity either in the half-plane or in a two dimensional bounded domain.
Under the necessary uniform Kreiss Lopatinskii condition we construct here a dissipative Kreiss symmetrizer of our problem; actually, due to the characteristic boundary and the lack of a technical assumption given by T. Ohkubo, the main difficulty consists of building the dissipative symmetrizer near some special "boundary points"
L^p-boundedness for pseudodifferential operators with non smooth symbols and applications
No full textStarting from a general formulation of the characterization by dyadic crowns of Sobolev spaces, the authors give a result of L^p continuity for pseudodifferential operators whose symbol a(x, ξ) is non smooth with respect to x and whose derivatives with respect to ξ have a decay of order ρ with 0<ρ≤1. The algebra property for some classes of weighted Sobolev spaces is proved and an application to multi - quasi - elliptic semilinear equations is given
Weakly well posed hyperbolic initial-boundary value problems with non characteristic boundary
No full textWe study the mixed initial-boundary value problem for a linear hyperbolic system
with non characteristic boundary. We assume the problem to be “weakly” well posed, in the sense
that a unique L2-solution exists, for sufficiently smooth data, and obeys an a priori energy estimate
with a finite loss of regularity. This is the case of problems that do not satisfy the uniform Kreiss-
Lopatinski ̆ı condition. Under the assumption of the loss of one tangential derivative, we obtain the
Sobolev regularity of solutions, provided the data are sufficiently smoot
Multi-anisotropic Gevrey classes and ultradistributions
No full textWe consider a relevant generalization of the standard Gevrey classes, the so-called multi-anisotropic spaces, defined in terms of a given complete polyhedron. With respect to the previous literature on the subject, we concentrate here in the study of the topology. It is defined as inductive and projective limit of Banach spaces, in two equivalent ways, based on the estimates on the derivatives and on the Fourier transform, respectively. We consequently introduce the dual space, the class of the
multi-anisotropic ultradistributions, of which we give different characterizations, study topological and algebraic properties and present some applications
L^p-microlocal regularity for pseudodifferential operators of quasi-homogeneous type
Full text linkThe authors consider pseudodifferential operators whose symbols have decay at infinity of quasi-homogeneous type and study their behaviour on the wave front set of distributions in weighted Zygmund-Holder spaces and weighted Sobolev spaces in L-p-framework. Then microlocal properties for solutions to linear partial differential equations with coefficients in weighted Zygmund-Holder spaces are obtained
Inhomogeneous microlocal propagation of singularities in Fourier Lebesgue spaces
Full text linkIn the paper some results of microlocal continuity for pseudodifferential operators whose symbols belong to weighted Fourier Lebesgue spaces are given. Inhomogeneous local and microlocal propagation of singularities of Fourier Lebesgue type are then studied, with applications to some classes of semilinear equations
Weakly well posed characteristic hyperbolic problems
No full textWe present recent results about the mixed initial-boundary value problem for a linear hyperbolic system with characteristic boundary of constant multiplicity. We assume the problem to be ''weakly'' well posed, namely that a unique L^2-solution exists, for sufficiently smooth data, and obeys an a priori energy estimate with a finite loss of conormal regularity. Under the assumption of the loss of one conormal derivative, we obtain the regularity of solutions in the natural framework of the anisotropic Sobolev spaces, provided the data are sufficiently smooth
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