## Radial limits of capillary surfaces at corners

##### Citation

*Entekhabi, Mozhgan (Nora); Lancaster, Kirk E. Radial limits of capillary surfaces at corners. Pacific Journal of Mathematics, vol. 288:no. 1:pp 55–67*

##### Abstract

Consider a solution f is an element of C-2(Omega) of a prescribed mean curvature equation
div del f/root 1+vertical bar del f vertical bar(2) = 2H (x, f) in Omega subset of R-2,
where Omega is a domain whose boundary has a corner at O = (0; 0) epsilon partial derivative Omega and the angular measure of this corner is 2 alpha, for some alpha epsilon(0,pi). Suppose sup(x epsilon Omega) vertical bar f(x)vertical bar and sup(x epsilon Omega) vertical bar H (x; f(x))vertical bar are both finite. If alpha > pi/2, then the (nontangential) radial limits of f at O, namely
Rf(theta) = lim(r down arrow 0) (r cos theta, r sin theta)
were recently proven by the authors to exist, independent of the boundary behavior of f onand to have a specific type of behavior.
Suppose partial derivative Omega 4; 2 , the contact angle gamma(.) / that the graph of f makes with one side of @ has a limit (denoted gamma(2)) at O and
pi - 2 alpha < gamma 2 <2 alpha.
We prove that the (nontangential) radial limits of f at O exist and the radial limits have a specific type of behavior, independent of the boundary behavior of f on the other side of partial derivative Omega. We also discuss the case 2 0; 2 and the displayed inequalities do not hold.

##### Description

Click on the DOI link to access the article (may not be free).
All articles published by MSP become open access after five years past publication (meaning on the fifth January 1st after the publication date). The Annals of Mathematics, while not published by MSP, also becomes open access after five years.