A domain description and Green's function estimates up to the boundary for elliptic operator with singular potential

作者：Serov V S^*; Kyllonen U M

来源：Journal of Mathematical Analysis and Applications, 2010, 366(1): 11-23.

DOI：10.1016/j.jmaa.2010.01.018

• Elliptic operator
• Fundamental solution
• Green's function

We consider the Friedrichs extension of the operator A = A(0) + q(x), defined on a bounded domain Omega in R(n), n >= 1. For n = 1, we assume that Omega = inverted right perpendicular, binverted left perpendicular. Here A(0) = A(0)(x, D) is an elliptic operator of order 2m with bounded smooth coefficients and q a function in L(p)(Omega). Under some assumptions for q we obtain the uniform up to the boundary estimates for the Green's function of the Friedrichs extension of the operator A + lambda l, for lambda sufficiently large. Under some stronger assumptions for q we give a description for the domain of the Friedrichs extension of A.

• 出版日期2010-6-1