Riemannsche Flächen mit Eigenwerten in (0, ...).
Riesz basis generation, eigenvalues distribution, and exponential stability for a Euler-Bernoulli beam with joint feedback control.
Using an abstract result on Riesz basis generation for discrete operators in general Hilbert spaces, we show, in this article, that the generalized eigenfunctions of an Euler-Bernoulli beam equation with joint linear feedback control form a Riesz basis for the state space. The spectrum-determined growth condition is hence obtained. Meanwhile, the exponential stability as well as the asymptotic expansion of eigenvalues are also readily obtained by a straightforward computation.
Riesz basis property of Timoshenko beams with boundary feedback control.
Riesz means for the eigenfunction expansions for a class of hypo-elliptic differential operators
We study the Riesz means for the eigenfunction expansions of a class of hypoelliptic differential operators on the Heisenberg group. The operators we consider are homogeneous with respect to dilations and invariant under the action of the unitary group. We obtain convergence results in norm, at Lebesgue points and almost everywhere. We also prove localization results.
Riesz means of bounded states and semi-classical limit connected with a Lieb-Thirring conjecture. II
Riesz potentials for Korteweg-de Vries solitons and Sturm-Liouville problems.
Riesz transform on manifolds and heat kernel regularity
Right inverses for partial differential operators on Fourier hyperfunctions
We characterize the partial differential operators P(D) admitting a continuous linear right inverse in the space of Fourier hyperfunctions by means of a dual (Ω̅)-type estimate valid for the bounded holomorphic functions on the characteristic variety near . The estimate can be transferred to plurisubharmonic functions and is equivalent to a uniform (local) Phragmén-Lindelöf-type condition.
Rigidity for the hyperbolic Monge-Ampère equation
Some properties of nonlinear partial differential equations are naturally associated with the geometry of sets in the space of matrices. In this paper we consider the model case when the compact set is contained in the hyperboloid , where , the set of symmetric matrices. The hyperboloid is generated by two families of rank-one lines and related to the hyperbolic Monge-Ampère equation . For some compact subsets containing a rank-one connection, we show the rigidity property of by imposing...
Rigidity of generalized laplacians and some geometric applications. (Summary).
Rigidity of generalized laplacians and some geometric applications.
Rigorous derivation of Korteweg-de Vries-type systems from a general class of nonlinear hyperbolic systems
Rigorous derivation of Korteweg-de Vries-type systems from a general class of nonlinear hyperbolic systems
In this paper, we study the long wave approximation for quasilinear symmetric hyperbolic systems. Using the technics developed by Joly-Métivier-Rauch for nonlinear geometrical optics, we prove that under suitable assumptions the long wave limit is described by KdV-type systems. The error estimate if the system is coupled appears to be better. We apply formally our technics to Euler equations with free surface and Euler-Poisson systems. This leads to new systems of KdV-type.
Rigorous numerics for the Cahn-Hilliard equation on the unit square.
Rigorous resonant 1-d nonlinear geometric optics
Rigorous results and conjectures on stationary space-periodic 2D turbulence
We discuss recent results on the inviscid limits for the randomly forced 2D Navier-Stokes equation under periodic boundary conditions, their relevance for the theory of stationary space periodic 2D turbulence and some related conjectures.
Ring source potentials in two superposed fluids separated by an inertial surface.
Risolubilità e ipoellitticità per equazioni differenziali a derivate parziali semilineari con caratteristiche multiple
Risoluzione di una congettura di De Giorgi in
Risoluzione, in , della II congettura di De Giorgi