A priori bounds for graphs with prescribed curvature. (English) Zbl 0714.53008

Trudinger, Neil S.

Analysis, et cetera, Res. Pap. in Honor of J. Moser’s 60th Birthd., 667-676 (1990).

[For the entire collection see Zbl 0688.00009.]
The author establishes an a priori estimate of the \(C^ 0\)-norm of a solution to the equation \(H_ m(u)=H\) in a bounded domain \(\Omega \subset {\mathbb{R}}^ n\); here \(H_ m\) is the m-th elementary symmetric function of the principal curvatures of the graph of \(u=u(x)\), \(x\in {\bar \Omega}\). The estimate is established under conditions on H and \(\Omega\) generalizing an analogous condition known in the case of mean curvature \(H_ 1\).

Reviewer: V.I.Oliker

MSC:

53A07	Higher-dimensional and -codimensional surfaces in Euclidean and related \(n\)-spaces
53C40	Global submanifolds
35J60	Nonlinear elliptic equations

Keywords:

a priori estimate; principal curvatures; graph; mean curvature

Citations:

Zbl 0688.00009