A unique continuation property on the boundary for solutions of elliptic equations

Zhi Ren Jin
1993 Transactions of the American Mathematical Society  
We prove the following conclusion: if « is a harmonic function on a smooth domain fl in R" , n > 3 , or a solution of a general second-order linear elliptic equation on a domain Q in R2 , and if there are X(¡ 6 d£l and constants a, b > 0 suchthat \u(x)\ < aexp{-6/l*-*ol} for x e £2 , |x-*ol small, then u = 0 in Í2 . The decay rate in our results is best possible by the example that u = real part of exp{-l/zQ} , 0 < a < 1 , is harmonic but not identically zero in the right complex half-plane.
doi:10.1090/s0002-9947-1993-1085944-3 fatcat:qn2fofiu7jdi3bkdmwdcug4ovi