[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.11568/kjm.2018.26.4.747

A MAXIMUM PRINCIPLE FOR NON-NEGATIVE ZEROTH ORDER COEFFICIENT IN SOME UNBOUNDED DOMAINS

Cho, Sungwon (Department of Mathematics Education, Gwangju national university of education)

Publication Information

Korean Journal of Mathematics / v.26, no.4, 2018 , pp. 747-756 More about this Journal

Abstract

We study a maximum principle for a uniformly elliptic second order differential operator in nondivergence form. We allow a bounded positive zeroth order coefficient in a certain type of unbounded domains. The results extend a result by J. Busca in a sense of domains, and we present a simple proof based on local maximum principle by Gilbarg and Trudinger with iterations.

Keywords

Maximum principle in unbounded domains; Second-order elliptic equation; Measurable coefficients; A priori estimates; Behavior of subsolution at infinity;

Citations & Related Records

Reference

1	H. Berestycki, L. Nirenberg, S. R. S. Varadhan, The principal eigenvalue and maximum principle for second-order elliptic operators in general domains, Comm. Pure Appl. Math. 47 (1) (1994), 47-92. DOI
2	J. Busca Existence results for Bellman equations and maximum principles in unbounded domains, Comm. Partial Differential Equations 24 (11-12) (1999), 2023-2042. DOI
3	X. Cabre, Estimates for Solutions of Elliptic and Parabolic Problems, Ph.D. Thesis. (1994), Courant Institute, New York University, U.S.
4	X. Cabre, On the Alexandroff-Bakel'man-Pucci estimate and the reversed Holder inequality for solutions of elliptic and parabolic equations, Comm. Pure Appl. Math. 48 (5) (1995), 539-570. DOI
5	L. C. Evans, Partial Differential Equations, Am. Math. Soc., Providence, RI, 1998
6	D. Gilbarg, N. Trudinger, Elliptic Partial Differential Equations of Second Order, Reprint of the 1998 edition. Classics in Mathematics. Springer-Verlag, Berlin, 2001.
7	O.A. Ladyzhenskaya and N.N. Ural'tseva, Linear and Quasilinear Elliptic Equations, "Nauka", Moscow, 1964 in Russian; English transl.: Academic Press, New York, 1968; 2nd Russian ed. 1973.
8	E. M. Landis, Second Order Equations of Elliptic and Parabolic Type, "Nauka", Moscow, 1971 in Russian; English transl.: Amer. Math. Soc., Providence, RI, 1997.