Le Matematiche (Dipartimento di Matematica e Informatica, Università degli Studi di Catania)
Not a member yet
1189 research outputs found
Sort by
POTENTIAL ANALYSIS FOR A CLASS OF DIFFUSION EQUATIONS: A GAUSSIAN BOUNDS APPROACH
Get PDFLet H be a linear second order partial differential operator with non-negative characteristic form in a strip S ⊂ R^N ×R. We assume that H as a fundamental solution, smooth out of its poles and bounded from above and from below by Gaussian kernels modeled on subriemannian doubling distances in R^N. Under these assumptions we show that H endows S with a structure of β-harmonic space. This allows us to study boundary value problems for L with a Perron-Wiener-Brelot-Bauer method, and to obtain pointwise regularity estimates at the boundary in terms of Wiener series modeled on the Gaussian kernels. Our analysis includes the proof of a scale invariant Harnack inequality for nonnegative solutions. We also show an application to the real hypersurphaces of C^{n+1} with given Levi-curvature.Let H be a linear second order partial differential operator with non-negative characteristic form in a strip S ⊂ RN ×R. We assume that H asa fundamental solution, smooth out of its poles and bounded from above and from below by Gaussian kernels modeled on subriemannian doubling distances in RN. Under these assumptions we show that H endows S with a structure of β-harmonic space. This allows us to study boundary value problems for L with a Perron-Wiener-Brelot-Bauer method, and to obtain pointwise regularity estimates at the boundary in terms of Wiener series modeled on the Gaussian kernels. Our analysis includes the proof of a scale invariant Harnack inequality for nonnegative solutions. We also show an application to the real hypersurphaces of Cn+1 with given Levi-curvature
HARNACK INEQUALITY FOR HARMONIC FUNCTIONS RELATIVE TO A NONLINEAR P-HOMOGENEOUS RIEMANNIAN DIRICHLET FORM
Get PDFWe consider a measure valued map α(u) defined on D where D is a subspace of L^p(X,m) with X a locally compact Hausdorff topological space with a distance under which it is a space of homogeneous type. Under assumptions of convexity, Gateaux differentiability and other assumptions on α which generalize the properties of the energy measure of a Dirichlet form, we prove the Holder continuity of the local solution u of the problem ∫Xµ(u,v)(dx) = 0 for each v belonging to a suitable space of test functions, where µ(u,v) =< α\u27(u),v >.We consider a measure valued map α(u) defined on D where D isa subspace of L^p(X,m) with X a locally compact Hausdorff topological space with a distance under which it is a space of homogeneous type. Under assumptions of convexity, Gateaux differentiability and otherassumptions on α which generalize the properties of the energy measure of a Dirichlet form, we prove the Holder continuity of the local solution u of the problem IXµ(u,v)(dx) = 0 for each v belonging to a suitable space of test functions, where µ(u,v) =< α\u27(u),v >
ONE-DIMENSIONAL MOTION OF A MATERIAL WITH A STRAIN THRESHOLD
Get PDFWe consider the one-dimensional shearing motion of a material exhibiting elastic behaviour when the stress is below some threshold. The threshold represents a limit to the deformability, i.e. no further deformation can occur on increasing the stress. The mathematical formulation leads to a free boundary problem for the wave equation, whose structure depends on whether the stress (and the velocity) are continuous across the propagating interface for the strain threshold .Local existence and uniqueness are proved for the continuous case (in which the interface propagation is subsonic). Some explicit solutions are calculated for another case (with a supersonic interface). It is shown that the model with strain threshold is never the limit of hyperelastic systems.We consider the one-dimensional shearing motion of a material exhibiting elastic behaviour when the stress is below some threshold. The threshold represents a limit to the deformability, i.e. no further deformation can occur on increasing the stress. The mathematical formulation leads to a free boundary problem for the wave equation, whose structure depends on whether the stress (and the velocity) are continuous across the propagating interface for the strain threshold .Local existence and uniqueness are proved for the continuous case (inwhich the interface propagation is subsonic). Some explicit solutions arecalculated for another case (with a supersonic interface). It is shown thatthe model with strain threshold is never the limit of hyperelastic systems
Sur les idéaux d\u27une algèbre de Beurling généralisée
No full textIn this paper, we characterize the closed ideals of locally m-convex algebras as the linear closed subspaces that are invariant under translation. We also give a weighted algebra analogues of the classical theorems of N. Wiener and P. Lé́ vy on absolutely convergent Fourier series
ON THE SETS OF BOUNDEDNESS OF SOLUTIONS TO DEGENERATE FOURTH-ORDER EQUATIONS WITH STRENGTHENINGLY MONOTONE PRINCIPAL PARTS, ABSORPTION AND L1-DATA
Get PDFWe consider the Dirichlet problem for a class of degenerate nonlinear elliptic fourth-order equations with strengtheningly monotone principal parts, absorbing lower-order terms and L1-right-hand sides. We establish existence of solutions of the given problem bounded on the sets where the behaviour of the data of the problem is regular enough.We consider the Dirichlet problem for a class of degenerate nonlinearelliptic fourth-order equations with strengtheningly monotone principalparts, absorbing lower-order terms and L1-right-hand sides. We establish existence of solutions of the given problem bounded on the sets where the behaviour of the data of the problem is regular enough
SINGULAR DIMENSION OF SPACES OF REAL FUNCTIONS
Get PDFLet X be a space of measurable real functions defined on a fixed open set Ω ⊆ R^N . It is natural to define the singular dimension of X as the supremum of Hausdorff dimension of singular sets of all functions in X.We say that f ∈ X is a maximally singular function in X if the Hausdorff dimension of its singular set is the largest possible. The paper discusses recent results about singular dimension of Banach spaces of functions, existence and density of maximally singular functions, and provides some open problems.Let X be a space of measurable real functions defined on a fixed openset Ω C RN. It is natural to define the singular dimension of X as thesupremum of Hausdorff dimension of singular sets of all functions in X.We say that f C X is a maximally singular function in X if the Hausdorffdimension of its singular set is the largest possible. The paper discusses recent results about singular dimension of Banach spaces of functions, existence and density of maximally singular functions, and provides some open problems
IN MEMORY OF GAETANO FICHERA
Get PDFDear Dr. Matelda Fichera, Prof. Dr. Maria Pia Colautti, Dr. Anna MariaFichera, Dr. Massimo Fichera,Gaetano Fichera passed away at the age of 74 June 1st just 10 years ago. He left behind his dear wife Dr. Mathelda Fichera after 44 years of happy togetherness - and the world of mathematics.Dear Dr. Matelda Fichera, Prof. Dr. Maria Pia Colautti, Dr. Anna MariaFichera, Dr. Massimo Fichera,Gaetano Fichera passed away at the age of 74 June 1st just 10 years ago. He left behind his dear wife Dr. Mathelda Fichera after 44 years of happy to- getherness - and the world of mathematics
ON GENERALIZED DERIVATIVES AND FORMAL POWERS FOR PSEUDOANALYTIC FUNCTIONS
Get PDFWe consider pseudoanalytic functions depending on two or three real variables. They are characterized by the corresponding Bers-Vekua equations. In the case of two dimensions we use the complex notation whereas for the case of three variables the concept of complex quaternions serves for our investigations. In a particular plane case we give an explicit representation of formal powers with which a complete system of solutions of the corresponding Bers-Vekua equation can be given. By an example we show how the concept of formal powers may also be applied to the case of three variables.We consider pseudoanalytic functions depending on two or three realvariables. They are characterized by the corresponding Bers-Vekua equations. In the case of two dimensions we use the complex notation whereas for the case of three variables the concept of complex quaternions serves for our investigations. In a particular plane case we give an explicit representation of formal powers with which a complete system of solutions of the corresponding Bers-Vekua equation can be given. By an example we show how the concept of formal powers may also be applied to the case of three variables
WIENER CRITERION AT THE BOUNDARY RELATED TO P-HOMOGENEOUS STRONGLY LOCAL DIRICHLET FORMS
Get PDFWe state a Wiener criterion at the boundary related to p-homogeneous strongly local Riemannian type Dirichlet forms.We state a Wiener criterion at the boundary related to p-homogeneousstrongly local Riemannian type Dirichlet forms
ON BERNOULLI BOUNDARY VALUE PROBLEM
Get PDFWe give a constructive proof of the existence and uniqueness of the solution, under certain conditions, by Picard’s iteration. Moreover Newton’s iteration method is considered for the numerical computation of the solution.We give a constructive proof of the existence and uniqueness of thesolution, under certain conditions, by Picard’s iteration. MoreoverNewton’s iteration method is considered for the numerical computation of the solution