A Sharp Decay Estimate for Positive Nonlinear Waves

A Sharp Decay Estimate for Positive Nonlinear Waves

We consider a strictly hyperbolic, genuinely nonlinear system of conservation laws in one space dimension. A sharp decay estimate is proved for the positive waves in an entropy weak solution. The result is stated in terms of a partial ordering among positive measures, using symmetric rearrangements and a comparison with a solution of Burgers’ equation with impulsive sources. 1 Introduction Cons...

A Sharp Bilinear Restriction Estimate for Paraboloids

X iv :m at h/ 02 10 08 4v 2 [ m at h. C A ] 1 3 D ec 2 00 2 Abstract. Recently Wolff [28] obtained a sharp L2 bilinear restriction theorem for bounded subsets of the cone in general dimension. Here we adapt the argument of Wolff to also handle subsets of “elliptic surfaces” such as paraboloids. Except for an endpoint, this answers a conjecture of Machedon and Klainerman, and also improves upon ...

A Sharp Maximal Function Estimate for Vector-Valued Multilinear Singular Integral Operator

We establish a sharp maximal function estimate for some vector-valued multilinear singular integral operators. As an application, we obtain the $(L^p, L^q)$-norm inequality for vector-valued multilinear operators.

Utility of Amplitudes of Positive Sharp Waves and Fibrillation Potentials

Objective: Fibrillation potentials and positive sharp waves are pathologic spontaneous potentials which originate disconnection anywhere betweenanterior hornof medulla spinalisto muscle fiber in the motor unit. In clinical practice, the presence and if present the intensity of the spontaneous denervation potentials has been evaluated. In this study, the relations between their amplitudes and pa...

On Nonlinear Water Waves in a Channel