Oblique derivative problem for elliptic second-order semi-linear equations in a domain with a conical boundary point

• Main Authors: Mariusz Bodzioch, Mikhail Borsuk
• Format: Article
• Language: English
• Published: Texas State University 2018-03-01
• Series: Electronic Journal of Differential Equations
• Subjects: Elliptic equations; oblique problem; conical points
• Online Access: http://ejde.math.txstate.edu/Volumes/2018/69/abstr.html

This article concerns the oblique boundary value problem for elliptic semi-linear equations in a domain with a conical point on the boundary. We investigate the asymptotic behavior of strong solutions near a boundary conical point. New regularity theorems are established under the least possible assumptions on the equation coefficients. The investigation of asymptotic properties of solutions can be used to obtain new solvability theorems. The results obtained in this paper are extensions of our previous results to a wider class of elliptic equations.