Properties of superharmonic functions satisfying nonlinear inequalities in nonsmooth domains

DOI Web Site 3 Citations 28 References

Search this article

Abstract

In a uniform domain Ω, we present a certain reverse mean value inequality and a Harnack type inequality for positive superharmonic functions satisfying a nonlinear inequality -Δu(x) ≤ cδΩ(x)-αu(x)p for x ∈ Ω, where c > 0, α ≥ 0 and p > 1 and δΩ(x) is the distance from a point x to the boundary of Ω. These are established by refining a boundary growth estimate obtained in our previous paper (2008). Also, we apply them to show the existence of nontangential limits of quotients of such functions and to give an extension of a certain minimum principle studied by Dahlberg (1976).

Journal

Citations (3)*help

See more

References(28)*help

See more

Related Projects

See more

Keywords

Details 詳細情報について

Report a problem

Back to top