Fractal Weyl laws for quantum resonances
Fractional Sobolev norms and structure of Carnot-Carathéodory balls for Hörmander vector fields
We study the notion of fractional -differentiability of order along vector fields satisfying the Hörmander condition on . We prove a modified version of the celebrated structure theorem for the Carnot-Carathéodory balls originally due to Nagel, Stein and Wainger. This result enables us to demonstrate that different -norms are equivalent. We also prove a local embedding , where q is a suitable exponent greater than p.
Fredholm properties of elliptic operators on ℝⁿ [Book]
Fredholm property for a parameter dependent second order operator differential equation.
Fredholmness of an abstract differential equation of elliptic type.
Free boundary problems and transonic shocks for the Euler equations in unbounded domains
We establish the existence and stability of multidimensional transonic shocks (hyperbolic-elliptic shocks), which are not nearly orthogonal to the flow direction, for the Euler equations for steady compressible potential fluids in unbounded domains in . The Euler equations can be written as a second order nonlinear equation of mixed hyperbolic-elliptic type for the velocity potential. The transonic shock problem can be formulated into the following free boundary problem: The free boundary is the...
Free Boundary Problems with Nonlinear Source Terms.
From h to p Efficiently: Selecting the Optimal Spectral/hp Discretisation in Three Dimensions
There is a growing interest in high-order finite and spectral/hp element methods using continuous and discontinuous Galerkin formulations. In this paper we investigate the effect of h- and p-type refinement on the relationship between runtime performance and solution accuracy. The broad spectrum of possible domain discretisations makes establishing a performance-optimal selection non-trivial. Through comparing the runtime of different implementations...
From repeated games to brownian games
Front d’onde à l’infini pour l’équation de Schrödinger
Full -regularity for minimizers of integral functionals with -growth.
Fully nonlinear second order elliptic equations : recent development
Fully nonlinear second order elliptic equations with large zeroth order coefficient
We prove the existence of classical solutions to certain fully non-linear second order elliptic equations with large zeroth order coefficient. The principal tool is an a priori estimate asserting that the -norm of the solution cannot lie in a certain interval of the positive real axis.
Function spaces and spectra of elliptic operators on a class of hyperbolic manifolds
The paper deals with quarkonial decompositions and entropy numbers in weighted function spaces on hyperbolic manifolds. We use these results to develop a spectral theory of related Schrödinger operators in these hyperbolic worlds.
Function theory for a Beltrami algebra.
Functional determinants and geometry .
Functional determinants and geometry (Erratum).
Functionals with linear growth in the calculus of variations. II.
Functionals with linear growth in the calculus of variations. I.
Functions of four variables which satisfy both the heat equation and the Laplace equation in three variables - II