243 research outputs found
Some Zaremba-Hopf-Oleinik Boundary Comparison Principles at Characteristic Points
No full textWe investigate the so-called Hopf lemma for certain degenerate-elliptic equations at characteristic boundary points of bounded open sets. For such equations, the validity of the Hopf lemma is related to the fact that the boundary of the open set reflects the underlying geometry of the specific operator. We present here some recent results obtained in [21] in collaboration with V. Martino. Our main focus is on conditions on the boundary which are stable by changing our operators in some particular classes, for example in the class of horizontally elliptic operators in non-divergence form. We also study what happens to these conditions for degenerate operators with first order terms
Problemi di simmetria per palle della gauge nel gruppo di Heisenberg
No full textIn this note we focus on possible characterizations of gauge-symmetric functions in the Heisenberg group. We discuss a family of inverse problems in potential theory relating solid and surface weighted mean-value formulas, and we show a partial solution to such problems. To this aim, we review a uniqueness result for gauge balls obtained with V. Martino in [23] by means of overdetermined problems of Serrin-type. The class of competitor sets we consider enjoys partial symmetries of toric and cylindrical type.In questa nota vengono discusse possibili caratterizzazioni di funzioni gauge-simmetriche nel gruppo di Heisenberg. Viene mostrata una soluzione parziale ad una famiglia di problemi inversi legati ad opportune formule di media solida e superficiale pesate per funzioni armoniche rispetto al subLaplaciano di Heisenberg. A questo scopo, viene presentato un risultato di unicità ottenuto in [23] con V. Martino per problemi sovradeterminati di tipo Serrin in questo contesto. La classe di insiemi considerata gode di proprietà di simmetria parziale di tipo torico e cilindrico
Feeling the heat in a group of Heisenberg type
No full textIn this paper we use the heat equation in a group of Heisenberg type G to provide a unified treatment of the two very different extension problems for the time independent pseudo-differential operators Ls and Ls,
Some global Sobolev inequalities related to Kolmogorov-type operators
No full textIn this note we review a recent result in [17] in collaboration with N. Garofalo, where we establish global versions of Hardy-Littlewood-Sobolev inequalities attached to hypoelliptic equations of Kolmogorov type. The relevant Sobolev spaces are defined through the fractional powers of the operator under consideration. We outline the main steps of the semigroup approach we adopt.Viene qui presentato un recente risultato ottenuto in [17] in collaborazione con N. Garofalo, in cui si dimostrano disuguaglianze globali di tipo Hardy-Littlewood-Sobolev relative ad una classe di operatori ipoellittici di tipo Kolmogorov. Nell'approccio adottato gli spazi di Sobolev sono definiti attraverso le potenze frazionarie dell'operatore in questione
A Reissner–Mindlin limit analysis model for out-of-plane loaded running bond masonry walls
No full textEarthquake surveys have demonstrated that the lack of out-of-plane strength is a primary cause of failure in many traditional forms of masonry. Moreover, bearing walls are relatively thick and, as a matter of fact, many codes of practice impose a minimal slenderness for them, as for instance the recent Italian O.P.C.M. 3431 [2005. Ulteriori modifiche ed integrazioni all’OPCM 3274/03 (in Italian) and O.P.C.M. 3274, 20/03/2003, Primi elementi in materia di criteri generali per la classificazione sismica del territorio nazionale e di normative tecniche per le costruzioni in zona sismica (in Italian)], in which the upper bound slenderness is fixed respectively equal to 12 for artificial bricks and 10 for natural blocks masonry. In this context, a formulation at failure for regular assemblages of bricks based both on homogenization and Reissner–Mindlin theory seems particularly attractive. In this paper a kinematic limit analysis approach under the hypotheses of the thick plate theory is developed for the derivation of the macroscopic failure surfaces of masonry out-of-plane loaded. The behavior of a 3D system of blocks connected by interfaces is identified with a 2D Reissner–Mindlin plate. Infinitely resistant blocks connected by interfaces (joints) with a Mohr–Coulomb failure criterion with tension cut-off and compressive cap are considered. Finally, an associated flow rule for joints is adopted. In this way, the macroscopic masonry failure surface is obtained as a function of the macroscopic bending moments, torsional moments and shear forces by means of a linear programming problem in which the internal power dissipated is minimized, once that a subclass of possible deformation modes is a priori chosen. Several examples of technical relevance are presented and comparisons with previously developed Kirchhoff–Love static [Milani, G., Lourenc ̧o, P.B., Tralli, A., 2006b. A homogenization approach for the limit analysis of out-of-plane loaded masonry walls. J. Struct. Eng. ASCE (in press)] and kinematic [Sab, K., 2003.Yield design of thin periodic plates by a homogenisation technique and an application to masonry walls. C.R. Mech. 331, 641–646] failure surfaces are provided. Finally, two meaningful structural examples are reported, the first concerning a masonry wall under cylindrical flexion, the second consisting of a rectangular plate with a central opening out-of-plane loaded. For both cases, the influence of the shear strength on the collapse load is estimated
A Reissner Mindlin limit analysis model for out-of-plane loaded running bond masonry walls
No full textEarthquake surveys have demonstrated that the lack of out-of-plane strength is a primary cause of failure in many traditional forms of masonry. Moreover, bearing walls are relatively thick and, as a matter of fact, many codes of practice impose a minimal slenderness for them, as for instance the recent Italian O.P.C.M. 3431 [2005. Ulteriori modifiche ed integrazioni all’OPCM 3274/03 (in Italian) and O.P.C.M. 3274, 20/03/2003, Primi elementi in materia di criteri generali per la classificazione sismica del territorio nazionale e di normative tecniche per le costruzioni in zona sismica (in Italian)], in which the upper bound slenderness is fixed respectively equal to 12 for artificial bricks and 10 for natural blocks masonry. In this context, a formulation at failure for regular assemblages of bricks based both on homogenization and Reissner-Mindlin theory seems particularly attractive. In this paper a kinematic limit analysis approach under the hypotheses of the thick plate theory is developed for the derivation of the macroscopic failure surfaces of masonry out-of-plane loaded. The behavior of a 3D system of blocks connected by interfaces is identified with a 2D Reissner-Mindlin plate. Infinitely resistant blocks connected by interfaces (joints) with a Mohr-Coulomb failure criterion with tension cut-off and compressive cap are considered. Finally, an associated flow rule for joints is adopted. In this way, the macroscopic masonry failure surface is obtained as a function of the macroscopic bending moments, torsional moments and shear forces by means of a linear programming problem in which the internal power dissipated is minimized, once that a subclass of possible deformation modes is a priori chosen. Several examples of technical relevance are presented and comparisons with previously developed Kirchhoff-Love static [Milani, G., Lourenco, P.B., Tralli, A., 2006b. A homogenization approach for the limit analysis of out-of-plane loaded masonry walls. J. Struct. Eng. ASCE (in press)] and kinematic [Sab, K., 2003.Yield design of thin periodic plates by a homogenisation technique and an application to masonry walls. C.R. Mech. 331, 641-646] failure surfaces are provided. Finally, two meaningful structural examples are reported, the first concerning a masonry wall under cylindrical flexion, the second consisting of a rectangular plate with a central opening out-of-plane loaded. For both cases, the influence of the shear strength on the collapse load is estimated
A Wiener test à la Landis for evolutive Hörmander operators
No full textIn this paper we prove a Wiener-type characterization of boundary regularity, in the spirit of a classical result by Landis, for a class of evolutive Hörmander operators. We actually show the validity of our criterion for a larger class of degenerate-parabolic operators with a fundamental solution satisfying suitable two-sided Gaussian bounds. Our condition is expressed in terms of a series of balayages or, (as it turns out to be) equivalently, Riesz-potentials
A Class of Nonlocal Hypoelliptic Operators and their Extensions
No full textIn this paper we study nonlocal equations driven by the fractional powers of hypoelliptic operators in the form Ku = Au -partial_t u = tr(Q nabla^2 u) + - partial_t u, introduced by Hormander in his 1967 hypoellipticity paper. We show that the nonlocal operators (-K)^s , (-A)^s can be realized as the Dirichlet-to-Neumann map of doubly-degenerate extension problems. We solve such problems in L^infty, in L^p for 1 = 0. In forthcoming works we use such calculus to establish some new Sobolev and isoperimetric inequalities
On the Minkowski Formula for Hypersurfaces in Complex Space Forms
No full textIn this paper, we discuss various Minkowski-type formulas for real hypersurfaces in complex space forms. In particular, we investigate the formulas suggested by the natural splitting of the tangent space. In this direction, our main result concerns a new kind of 2nd Minkowski formula
Nonlocal isoperimetric inequalities for Kolmogorov-Fokker-Planck operators
No full textIn this paper we establish optimal isoperimetric inequalities for a nonlocal perimeter adapted to the fractional powers of a class of Kolmogorov-Fokker-Planck operators which are of interest in physics. These operators are very degenerate and do not possess a variational structure. The prototypical example was introduced by Kolmogorov in his 1938 paper on Brownian motion and the theory of gases. Our work has been influenced by ideas of M. Ledoux in the local case
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