Renormalized solutions of elliptic equations with general measure data
Resolvent estimates in W -1,p for second order elliptic differential operators in case of mixed boundary conditions.
Resonant delocalization for random Schrödinger operators on tree graphs
We analyse the spectral phase diagram of Schrödinger operators on regular tree graphs, with the graph adjacency operator and a random potential given by random variables. The main result is a criterion for the emergence of absolutely continuous spectrum due to fluctuation-enabled resonances between distant sites. Using it we prove that for unbounded random potentials spectrum appears at arbitrarily weak disorder in an energy regime which extends beyond the spectrum of. Incorporating...
Reverse convolution inequalities and applications to inverse heat source problems.
Revisited isoperimetric inequalities for the p-capacity and application to the muskat problem
Riemann-Lebesgue properties of Green's functions with applications to inverse scattering.
Risoluzione, in , della II congettura di De Giorgi
Risultati di regolarità, stabilità, instabilità e biforcazione per un problema a frontiera libera
Robust a posteriori error estimates for finite element discretizations of the heat equation with discontinuous coefficients
In this work we derive a posteriori error estimates based on equations residuals for the heat equation with discontinuous diffusivity coefficients. The estimates are based on a fully discrete scheme based on conforming finite elements in each time slab and on the A-stable -scheme with . Following remarks of [Picasso, Comput. Methods Appl. Mech. Engrg. 167 (1998) 223–237; Verfürth, Calcolo 40 (2003) 195–212] it is easy to identify a time-discretization error-estimator and a space-discretization...
Robust a posteriori error estimates for finite element discretizations of the heat equation with discontinuous coefficients
In this work we derive a posteriori error estimates based on equations residuals for the heat equation with discontinuous diffusivity coefficients. The estimates are based on a fully discrete scheme based on conforming finite elements in each time slab and on the A-stable θ-scheme with 1/2 ≤ θ ≤ 1. Following remarks of [Picasso, Comput. Methods Appl. Mech. Engrg. 167 (1998) 223–237; Verfürth, Calcolo40 (2003) 195–212] it is easy to identify a time-discretization error-estimator and a space-discretization...
Scattering on stratified media: the microlocal properties of the scattering matrix and recovering asymptotics of perturbations
The scattering matrix is defined on a perturbed stratified medium. For a class of perturbations, its main part at fixed energy is a Fourier integral operator on the sphere at infinity. Proving this is facilitated by developing a refined limiting absorption principle. The symbol of the scattering matrix determines the asymptotics of a large class of perturbations.
Scattering, scattering inverse et équations d'évolutions non linéaires
Scattering, transformations spectrales et équations d'évolution non linéaires
SDDEs limits solutions to sublinear reaction-diffusion SPDEs.
Second order parabolic equations and weak uniqueness of diffusions with discontinuous coefficients
We prove the unique solvability of parabolic equations with discontinuous leading coefficients in . Using this result, we establish the uniqueness of diffusion processes with time-dependent discontinuous coefficients.
Second order quasilinear functional evolution equations
We consider second order quasilinear evolution equations where also the main part contains functional dependence on the unknown function. First, existence of solutions in is proved and examples satisfying the assumptions of the existence theorem are formulated. Then a uniqueness theorem is proved. Finally, existence and some qualitative properties of the solutions in (boundedness and stabilization as ) are shown.
Semicontinuity and continuous selections for the multivalued superposition operator without assuming growth-type conditions
Let Ω be a measure space, and E, F be separable Banach spaces. Given a multifunction , denote by the set of all measurable selections of the multifunction , s ↦ f(s,x(s)), for a function x: Ω → E. First, we obtain new theorems on H-upper/H-lower/lower semicontinuity (without assuming any conditions on the growth of the generating multifunction f(s,u) with respect to u) for the multivalued (Nemytskiĭ) superposition operator mapping some open domain G ⊂ X into , where X and Y are Köthe-Bochner...
Semidiscrete central difference method in time for determining surface temperatures.
Semigroup approach to semilinear partial functional differential equations with infinite delay.
Semigroup approach to the Stefan problem with non-linear flux
Un problema di Stefan a due fasi con condizione di flusso non lineare sulla parte fissa della frontiera è affrontato mediante la teoria dei semigruppi di contrazione in . Si dimostra l'esistenza e l’unicità della soluzione nel senso di Crandall-Liggett e Bénilan.