On the behaviour of solutions of 
the Dirichlet problem for elliptic nondivergence second order
 equations near the conical boundary point

M. Borsuk

We investigate regularity of the solutions of the Dirichlet problem for second order linear and quasilinear uniformly elliptic nondivergence equations in a neighbourhood of a conical boundary point.

1. Agmon S., Douglis A., Nirenberg L. Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, I Comm. pure appl. math. – 1959. – V.12. – P.623–727.

2. 2. Azzam A. The behaviour of solutions of the Dirichlet problem for elliptic equations near angular point Indiana J. Pure and Appl. Math. – 1979. – V.10. – P.1453–1459.

3. Azzam A. Smoothness properties of bounded solutions of Dirichlet's problem for elliptic equations in regions with corners on the boundary Canad. Math. Bull. – 1980. – V.23, 194 2. – P.213–226.

4. Borsuk M.V. Best-possible estimates of solutions of the Dirichlet problem for linear elliptic nondivergence equations of second order in a neighbourhood of a boundary conical point Mat. Sb. – 1991. – V.182, 194 10. – P.1446–1462 (Russian).

5. Borsuk M.V. On the solvability of the first boundary value problem for elliptic second-order equations in a domain with a boundary conical point Math. phys., analysis, geometry. – 1997. – V.4, 194 4. – P.428–452 (Russian).

6. Courant R., Hilbert D. Methoden der mathematischen Physik B.I. – Springer-Verlag, 1931.

7. Gilbarg D., Trudinger N. Elliptic partial equations of second order. – Springer-Verlag, 1983.

8. Maz'ja V.G. Sobolev spaces. – Leningrad University, 1985.

	On the behaviour of solutions of the Dirichlet problem for elliptic nondivergence second order equations near the conical boundary point
Author	M. Borsuk Department of Mechanics and Mathematics, Ivan Franko State University of Lviv
Abstract	We investigate regularity of the solutions of the Dirichlet problem for second order linear and quasilinear uniformly elliptic nondivergence equations in a neighbourhood of a conical boundary point.
Keywords	Dirichlet problem, second-order linear and quasilinear equations, uniformly elliptic
DOI	doi:10.30970/ms.10.2.163-172
Reference	1. Agmon S., Douglis A., Nirenberg L. Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, I Comm. pure appl. math. – 1959. – V.12. – P.623–727. 2. 2. Azzam A. The behaviour of solutions of the Dirichlet problem for elliptic equations near angular point Indiana J. Pure and Appl. Math. – 1979. – V.10. – P.1453–1459. 3. Azzam A. Smoothness properties of bounded solutions of Dirichlet's problem for elliptic equations in regions with corners on the boundary Canad. Math. Bull. – 1980. – V.23, 194 2. – P.213–226. 4. Borsuk M.V. Best-possible estimates of solutions of the Dirichlet problem for linear elliptic nondivergence equations of second order in a neighbourhood of a boundary conical point Mat. Sb. – 1991. – V.182, 194 10. – P.1446–1462 (Russian). 5. Borsuk M.V. On the solvability of the first boundary value problem for elliptic second-order equations in a domain with a boundary conical point Math. phys., analysis, geometry. – 1997. – V.4, 194 4. – P.428–452 (Russian). 6. Courant R., Hilbert D. Methoden der mathematischen Physik B.I. – Springer-Verlag, 1931. 7. Gilbarg D., Trudinger N. Elliptic partial equations of second order. – Springer-Verlag, 1983. 8. Maz'ja V.G. Sobolev spaces. – Leningrad University, 1985.
Pages	163-172
Volume	10
Issue	2
Year	1998
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html

On the behaviour of solutions of the Dirichlet problem for elliptic nondivergence second order equations near the conical boundary point