A sharp Hölder estimate for elliptic equations in two variables

A sharp Hölder estimate for elliptic equations in two variables

We prove a sharp Hölder estimate for solutions of linear two-dimensional, divergence form elliptic equations with measurable coefficients, such that the matrix of the coefficients is symmetric and has unit determinant. Our result extends some previous work by Piccinini and Spagnolo [7]. The proof relies on a sharp Wirtinger type inequality.

Some sharp Hölder estimates for two-dimensional elliptic equations

We present some recent sharp estimates for the Hölder exponent of solutions of linear second order elliptic equations in divergence form with measurable coefficients. We apply such results to planar Beltrami equations, and we exhibit a mapping of the “angular stretching” type for which our estimates are attained.

A Sharp Bilinear Restriction Estimate for Elliptic Surfaces

X iv :m at h/ 02 10 08 4v 1 [ m at h. C A ] 7 O ct 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 th...

Complex Variables and Elliptic Equations

A new estimate for Hölder approximation by Bernstein operators

In this work we discuss the rate of simultaneous approximation of Hölder continuous functions by Bernstein operators, measured by Hölder norms with different exponents. We extend the known results on this topic.