Geometrical properties of level sets of solutions of elliptic problems. (English) Zbl 0597.35016

Kawohl, Bernhard

Nonlinear functional analysis and its applications, Proc. Summer Res. Inst., Berkeley/Calif. 1983, Proc. Symp. Pure Math. 45/2, 25-36 (1986).

Some geometric properties of level sets of solutions of elliptic problems are considered. Generalized concavity properties, such as convexity or star-shapedness of level sets, are known for some elliptic boundary value problems.
[For the entire collection see Zbl 0583.00018.]

Reviewer: W.Okrasiński

MSC:

35F20	Nonlinear first-order PDEs
35B50	Maximum principles in context of PDEs
35J25	Boundary value problems for second-order elliptic equations
26D10	Inequalities involving derivatives and differential and integral operators

Keywords:

geometrical properties; level sets of solutions