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Smooth local solutions to weingarten equations and -equations
In this paper, we study the existence of smooth local solutions to Weingarten
equations and -equations. We will prove that, for ,
the Weingarten equations and the -equations always have smooth local
solutions regardless of the sign of the functions in the right-hand side of the
equations. We will demonstrate that the associate linearized equations are
uniformly elliptic if we choose the initial approximate solutions
appropriately
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