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Spectral estimates and preconditioning for saddle point systems arising from optimization problemsTani, Mattia <1986> 19 May 2015 (has links)
In this thesis, we consider the problem of solving large and sparse linear systems of saddle point type stemming from optimization problems. The focus of the thesis is on iterative methods, and new preconditioning srategies are proposed, along with novel spectral estimtates for the matrices involved.
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Potential Analysis for Hypoelliptic Second Order PDEs with Nonnegative Characteristic FormAbbondanza, Beatrice <1986> 28 May 2015 (has links)
In this Thesis we consider a class of second order partial differential operators with non-negative characteristic form and with smooth coefficients. Main assumptions on the relevant operators are hypoellipticity and existence of a well-behaved global fundamental solution.
We first make a deep analysis of the L-Green function for arbitrary open sets and of its applications to the Representation Theorems of Riesz-type for L-subharmonic and L-superharmonic functions. Then, we prove an Inverse Mean value Theorem characterizing the superlevel sets of the fundamental solution by means of L-harmonic functions. Furthermore, we establish a Lebesgue-type result showing the role of the mean-integal operator in solving the homogeneus Dirichlet problem related to L in the Perron-Wiener sense. Finally, we compare Perron-Wiener and weak variational solutions of the homogeneous Dirichlet problem, under specific hypothesis on the boundary datum.
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Spectral analysis of a parameter-dependent sturm-liouville problemAnsaloni, Susanna <1981> 14 June 2007 (has links)
No description available.
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Asympotic behaviour of zero mass fields with spin 1 or 2 propagating on curved background spacetimesRaparelli, Tiziana <1979> 14 June 2007 (has links)
No description available.
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Analytic and gevrey (micro-)hypoellipticity for sums of squares: an FBI approachChinni, Gregorio <1980> 30 June 2008 (has links)
No description available.
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Approximations of Sobolev norms in Carnot groupsBarbieri, Davide <1979> 09 June 2008 (has links)
No description available.
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Maximum principle, mean value operators and quasi boundedness in non-euclidean settingsTommasoli, Andrea <1976> 30 June 2008 (has links)
This work deals with some classes of linear second order partial differential
operators with non-negative characteristic form and underlying non-
Euclidean structures. These structures are determined by families of locally
Lipschitz-continuous vector fields in RN, generating metric spaces of Carnot-
Carath´eodory type. The Carnot-Carath´eodory metric related to a family
{Xj}j=1,...,m is the control distance obtained by minimizing the time needed
to go from two points along piecewise trajectories of vector fields. We are
mainly interested in the causes in which a Sobolev-type inequality holds with
respect to the X-gradient, and/or the X-control distance is Doubling with
respect to the Lebesgue measure in RN. This study is divided into three
parts (each corresponding to a chapter), and the subject of each one is a
class of operators that includes the class of the subsequent one.
In the first chapter, after recalling “X-ellipticity” and related concepts
introduced by Kogoj and Lanconelli in [KL00], we show a Maximum Principle
for linear second order differential operators for which we only assume
a Sobolev-type inequality together with a lower terms summability. Adding
some crucial hypotheses on measure and on vector fields (Doubling property
and Poincar´e inequality), we will be able to obtain some Liouville-type results.
This chapter is based on the paper [GL03] by Guti´errez and Lanconelli.
In the second chapter we treat some ultraparabolic equations on Lie
groups. In this case RN is the support of a Lie group, and moreover we require that vector fields satisfy left invariance. After recalling some results
of Cinti [Cin07] about this class of operators and associated potential theory,
we prove a scalar convexity for mean-value operators of L-subharmonic
functions, where L is our differential operator.
In the third chapter we prove a necessary and sufficient condition of regularity,
for boundary points, for Dirichlet problem on an open subset of RN related
to sub-Laplacian. On a Carnot group we give the essential background
for this type of operator, and introduce the notion of “quasi-boundedness”.
Then we show the strict relationship between this notion, the fundamental
solution of the given operator, and the regularity of the boundary points.
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Teoria del potenziale non lineare e operatore di Schrödinger nei gruppi di CarnotImperato, Cristina <1980> 30 June 2008 (has links)
No description available.
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Analysis and optimal control for the phase-field transition system with non-homogeneous Cauchy-Neumann boundary conditionsBenincasa, Tommaso <1981> 25 May 2010 (has links)
No description available.
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Bistable elliptic equations with fractional diffusionCinti, Eleonora <1982> 05 July 2010 (has links)
This work concerns the study of bounded solutions to elliptic
nonlinear equations with fractional diffusion. More precisely, the aim of this
thesis is to investigate some open questions related to a conjecture of De Giorgi about the one-dimensional symmetry of bounded monotone solutions in all
space, at least up to dimension 8.
This property on 1-D symmetry of monotone solutions for
fractional equations was known in dimension n=2. The question remained open for n>2. In this work we establish new sharp energy estimates and one-dimensional symmetry property in dimension 3 for certain solutions of fractional equations. Moreover we study a particular type of solutions, called saddle-shaped solutions, which are the candidates to be global minimizers not one-dimensional in dimensions bigger or equal than 8. This is an open problem and it is expected to be true from the classical theory of minimal surfaces.
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