Vol. 88, No. 2, 1980

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ISSN: 0030-8730
Regularity of capillary surfaces over domains with corners

Leon M. Simon

Vol. 88 (1980), No. 2, 363–377
Abstract

Using the usual mathematical model (capillary surface equation with contact angle boundary condition) we discuss regularity of the equilibrium free surface of a fluid in a cylindrical container in case the container cross-section has corners.

It is shown that good regularity holds at a corner if the “corner angle” 𝜃 satisfies 0 < 𝜃 < π and 𝜃 + 2β > π, where 0 < β π∕2 is the contact angle between the fluid surface and the container wall.

It is known that no regularity holds in case 𝜃 + 2β < π, hence only the borderline case 𝜃 + 2β = π remains open.

Mathematical Subject Classification 2000
Primary: 49H05, 49H05
Secondary: 35R35, 58E12, 49F99
Milestones
Received: 26 March 1979
Published: 1 June 1980
Authors
Leon M. Simon