ON SOME PROPERTIES OF BARRIERS AT INFINITY FOR SECOND ORDER UNIFORMLY ELLIPTIC OPERATORS
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
We consider the boundary value problem with a Dirichlet condition for a second order linear uniformly elliptic operator in a non-divergence form. We study some properties of a barrier at in nity which was introduced by Meyers and Serrin to investigate a solution in an exterior domains. Also, we construct a modi ed barrier for more general domain than an exterior domain.
Abstract
We consider the boundary value problem with a Dirichlet condition for a second order linear uniformly elliptic operator in a non-divergence form. We study some properties of a barrier at in nity which was introduced by Meyers and Serrin to investigate a solution in an exterior domains. Also, we construct a modi ed barrier for more general domain than an exterior domain.
참고문헌 (11)
- S. Cho, "Holder regularity of solutions to second-order elliptic equations in nonsmooth domains", Bound. Value Probl., pp.24~ (2007)
- L.C. Evans, "Partial Differential Equations. Graduate Studies in Mathematics 19" (2010), Am. Math. Soc
- D. Gilbarg, "On isolated singularities of solutions of second order elliptic differential equations", J. Anal. Math., 4, pp.309~340 (1956)
- D. Gilbarg, "Elliptic Partial Differential Equations of Second Order" (1983), Springer-Verlag
- E. Hopf, "Elementare Bemerkungen ber die Lsungen partieller Differentialgleichungen zweiter Ordnung vom elliptischen Typus", Sitzungsberichte der Berliner Akademie der Wissenschaften, 19, pp.147~152 (1927)
- O.A. Ladyzhenskaya, "Linear and Quasilinear Elliptic Equations: "Nauka", Moscow, 1964 in Russian" (1973), Academic Press
- E.M. Landis, "Second Order Equations of Elliptic and Parabolic Type. "Nauka", Moscow, 1971 in Russian" (1997)
- G. Lieberman, "Second order parabolic differential equations" (1996), World Scientific
- N. Meyers, "The exterior Dirichlet problem for second order elliptic partial differential equations", J. Math. Mech., 9(4), pp.513~538 (1960)
- M. Protter, "Maximum principles in Differential equations" (1967), Prentice-Hall
- M.V. Safonov, "Non-divergence elliptic equations of second order with unbounded drift. Nonlinear partial differential equations and related topics. Dedicated to Nina U. Uraltseva on the occasion of her 75th birthday", pp.211~232 (2010)