A priori estimates for operational differential inclusions

A Priori Estimates for Fluid Interface Problems

We consider the regularity of an interface between two incompressible and inviscid fluids flows in the presence of surface tension. We obtain local in time estimates on the interface in H 3 2 k+1 and the velocity fields in H 3 2 . These estimates are obtained using geometric considerations which show that the Kelvin-Helmholtz instabilities are a consequence of a curvature calculation.

A priori estimates for excitable models

The reaction-diffusion system of Fitzhugh Nagumo is considered. The initialboundary problems with Neumann and Dirichlet conditions are analyzed. By means of an equivalent semilinear integrodifferential equation which characterizes several dissipative models of viscoelasticity, biology, and superconductivity, some results on existence, uniqueness and a priori estimates are deduced both in the li...

A Priori Estimates for Schrödinger Type Multipliers

We present an elementary proof of two a priori estimates for Schrödinger type multipliers on the circle. The first is an L4 − L2 inequality of Bourgain, while the second is a new L6 − L3/2 inequality. Estimates of this type are useful for the study of the Cauchy problem for Schrödinger type equations. The proofs are based on a counting argument and standard real and harmonic analysis techniques.

Optimal a priori estimates for interface problems

Uniqueness and a Priori Estimates

Under some conditions on f(u), we show that for small, the only solutions to the following elliptic equation u ? u + f(u) = 0 in ; u > 0 in ; @u @ = 0 on @ are constants, provided that R 3 is convex. The proof only uses integration by parts.