一类椭圆方程的边界唯一延拓性
Unique Continuation at the Boundary of Elliptic Equation
摘要
本文主要讨论了一类二阶椭圆方程Lu=-△u+Vu=0的弱解在连通凸区域边界上的唯一延拓性,并且证明了文[4]中提出的猜测在本文的情形同样成立.
In this paper, we study the relation with the weak solution of certain elliptic equation of second order and unique continuation at the boundary of connected, convex domains. And we prove the conjecture on [4] is also true at this case.
参考文献10
-
1KENIG C E. Restriction theorems, carleman estimates uniform sobolev inequalities and unique continuation [J]. Lecture Notes Math., 1384, 69-90.
-
2GAROFALO N, LIN F H. Monotonicity properties of variational integrals, Ap-weights and unique continuation [J]. Indiana Univ. Math. J., 1986, 35: 245-268.
-
3GAROFALO N, LIN F H. Unique continuation for elliptic operators: A geometric variational approach [J]. Comm. P. A. M., 1987, 40: 347-366.
-
4ADOFSSON V, ESCAURIAZA L, KENIG C E. Convex domains and unique continuation at the boundary [J]. Rev. Mat. Iberoamericana, 1995, 11: 513-525.
-
5ADOLFSSON V, ESCAURIAZA L. C1,α domains and Unique continuation at the boundary [J]. Comm. P.A.M., 1997, 50: 935-969.
-
6KUKAVICA I, KYSTROM K. Unique continuation on the boundary for Dini domains [J]. Proc. Amer. Math. Sco., 1998, 126: 441-446.
-
7GILBARG D, TRUDINGER N. Elliptic Partial Differential Equations of Second Order, 2nd ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] [M]. Springer, Berlin-New York, 1983, 224.
-
8CHIARENZA F, FABES E, GAROFALO N. Harnack's inequality of Schtodinger operators and the continuity of solutions [J]. Proc. Amer. Math. Soc., 1986, 98: 415-425.
-
9ALMGREN F J. Dirichlet's Problem for Multiple Valued Functions and the Regularity of Mass Minimizing Integral Currents [M]. Minimal Submanifolds and Geodesics (ed. M. Obata), North-Holland, 1979.
-
10NATANSON I P. Theory of Functions of a Real Variables [M]. Vol.I, Ungar Publishing Co., New York, 1964.