Archive for Rational Mechanics and Analysis

, Volume 155, Issue 3, pp 201–214

Removable Singularities for Fully Nonlinear Elliptic Equations

Authors

  • Denis A. Labutin
    • Departement der Mathematik¶ETH Zentrum¶8092 Zürich¶Switzerland

DOI: 10.1007/s002050000108

Cite this article as:
Labutin, D. Arch. Rational Mech. Anal. (2000) 155: 201. doi:10.1007/s002050000108

Abstract:

We obtain a removability result for the fully nonlinear uniformly elliptic equations F(D2u)+f(u)=0. The main theorem states that every solution to the equation in a punctured ball (without any restrictions on the behaviour near the centre of the ball) is extendable to the solution in the entire ball provided the function f satisfies certain sharp conditions depending on F. Previously such results were known for linear and quasilinear operators F. In comparison with the semi- or quasilinear theory the techniques for the fully nonlinear equations are new and based on the use of the viscosity notion of generalised solution rather than the distributional or the weak solutions.

Copyright information

© Springer-Verlag Berlin Heidelberg 2000