Nonlocal Robin problem in a plane domain with boundary corner point

Krzysztof Żyjewski

Abstract


We investigate the behavior of weak solutions to the nonlocal Robin problem for linear elliptic divergence second order equations in a neighborhood of the boundary corner point. We find an exponent of the solution decreasing rate under the minimal assumptions on the problem coefficients.

Keywords


Robin problem; boundary corner point;boundary-value problem

Mathematics Subject Classification


35J25; 35J60; 35J85; 35B65

References


Borsuk, M. andV. Kondratiev. "Elliptic boundary value problems of second order in piecewise smooth domains." North-Holland Mathematical Library, 69. Elsevier, 2006.

Gel’fand, I.M. and G.E. Shilov. "Generalized functions." vol. 1. New York-London: Academic Press, 1964.

Gilbarg, D. and N.S. Trudinger "Elliptic partial differential equations of second order." Berlin, Heidelberg, New York: Springer-Verlag, 1977. Revised Third Printing, 1998.

Gurevich, P.L. "Asymptotics of solutions for nonlocal elliptic problems in plane angles." J. Math. Sci. 120 (2004): 1295-1312.

Hardy, G.H., J.E. Littlewood and G. Pólya. "Inequalities" 1934. Cambridge: University Press, 1952.


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