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Research Report MRR99-035
Removable Singularities for Fully Nonlinear Elliptic Equations
Denis A. Labutin
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.
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