The sine-cosine method for the Davey-Stewartson equations.
The Singularity Expansion Method applied to the transient motions of a floating elastic plate
In this paper we propose an original approach for the simulation of the time-dependent response of a floating elastic plate using the so-called Singularity Expansion Method. This method consists in computing an asymptotic behaviour for large time obtained by means of the Laplace transform by using the analytic continuation of the resolvent of the problem. This leads to represent the solution as the sum of a discrete superposition of exponentially damped oscillating motions associated to the poles...
The Sobolev inequality on the Heisenberg group and the Yamabe problem on CR manifolds (d'après travaux avec J. M. Lee)
The solution of an axially symmetric boundary value problem of the generalized heat equation and its application in the technology of microschemes
The solution of embedding problems in the framework of GAPs with applications on nonlinear PDEs.
The solution of general KdV equation in a class of steplike functions.
The solution of inverse nonlinear elasticity problems that arise when locating breast tumours.
The solution of Kato's conjecture (after Auscher, Hofmann, Lacey, McIntosh and Tchamitchian)
Kato’s conjecture, stating that the domain of the square root of any accretive operator with bounded measurable coefficients in is the Sobolev space , i.e. the domain of the underlying sesquilinear form, has recently been obtained by Auscher, Hofmann, Lacey, McIntosh and the author. These notes present the result and explain the strategy of proof.
The solution of parabolic models by finite element space and -stable time discrezation
The Solution of Parabolic Partial Differential Equations by Boundary Value Methods
The solution of the initial value problem for the general dynamic equations in nonlinear elasticity under damping conditions
The solution of the Kato problem in two dimensions.
We solve, in two dimensions, the "square root problem of Kato". That is, for L ≡ -div (A(x)∇), where A(x) is a 2 x 2 accretive matrix of bounded measurable complex coefficients, we prove that L1/2: L12(R2) → L2(R2).[Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial (Madrid), 2002].
The Solution of the ...-Neumann Problem in a Strictly Pseudoconvex Siegel Domain.
The solution of the third problem for the Laplace equation on planar domains with smooth boundary and inside cracks and modified jump conditions on cracks.
The solution operator for a partial differential equation with delay
Viene dimostrata l’esistenza e l’unicità globale della soluzione di un’equazione funzionale in uno spazio di Hilbert e si caratterizza il generatore infinitesimale del semigruppo ad essa associato. Il risultato è applicato ad equazioni integrodifferenziali a derivate parziali di tipo parabolico in cui compaiono argomenti con ritardo (discreto e continuo) nelle derivate spaziali di ordine massimo.
The solutions of the quasilinear Keller-Segel system with the volume filling effect do not blow up whenever the Lyapunov functional is bounded from below
In [2] we proved two kinds of mechanisms of preventing the blow up in a quasilinear non-uniformly parabolic Keller-Segel systems. One of them was a priori boundedness from below of the Lyapunov functional. In fact, we were able to present a condition under which the Lyapunov functional is bounded from below and a solution exists globally. In the present paper we prove that whenever the Lyapunov functional is bounded from below the solution exists globally.
The solvability of non solvable operators
The space of exponentially decreasing entire functions and its application to solvability
The spaces of quantum states for some harmonic oscillator potentials on the punctured plane C∖{0}
We consider equivariant solutions of Schrödinger equations on C∖{0} with harmonic oscillator potentials. We determine the spaces of equivariant quantum states in three cases: for an isotropic and anisotropic harmonic oscillator potential centered at 0, and for a potential not centered at 0.
The spectral cutting problem