# A priori interior gradient bounds for solutions to elliptic Weingarten equations

@inproceedings{Korevaar1987API, title={A priori interior gradient bounds for solutions to elliptic Weingarten equations}, author={Nicholas J. Korevaar}, year={1987} }

- Published 1987
DOI:10.1016/s0294-1449(16)30357-2

Abstract In this paper a maximum principle approach is used to derive a priori interior gradient bounds for smooth solutions to the Weingarten equations f ( λ ) = ∑ i 1 i 2 … i k λ i 1 … λ i k = ψ ( x , u , v ) . Here λ = (λ 1 , …, λ n ) is the vector of principal curvatures of the graph of u at a point ( x , u ( x )) on the graph, with downward normal v . One requires a one-sided height bound ( u f is elliptic. The result generalizes what is known to be true for the prescribed mean curvature… CONTINUE READING

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