Author:
Banerjee Agnid,Manna Ramesh
Abstract
<p style='text-indent:20px;'>In this paper, we obtain new Carleman estimates for a class of variable coefficient degenerate elliptic operators whose constant coefficient model at one point is the so called Baouendi-Grushin operator. This generalizes the results obtained by the two of us with Garofalo in [<xref ref-type="bibr" rid="b10">10</xref>] where similar estimates were established for the "constant coefficient" Baouendi-Grushin operator. Consequently, we obtain: (ⅰ) a Bourgain-Kenig type quantitative uniqueness result in the variable coefficient setting; (ⅱ) and a strong unique continuation property for a class of degenerate sublinear equations. We also derive a subelliptic version of a scaling critical Carleman estimate proven by Regbaoui in the Euclidean setting using which we deduce a new unique continuation result in the case of scaling critical Hardy type potentials.</p>
Publisher
American Institute of Mathematical Sciences (AIMS)
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
Reference56 articles.
1. F. J. Almgren, Jr., Dirichlet's problem for multiple valued functions and the regularity of mass minimizing integral currents, Minimal Submanifolds and Geodesics, North-Holland, Amsterdam-New York, (1979), 1–6.
2. N. Aronszajn.A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order, J. Math. Pures Appl., 36 (1957), 235-249.
3. N. Aronszajn, A. Krzywicki, J. Szarski.A unique continuation theorem for exterior differential forms on Riemannian manifolds, Ark. Mat., 4 (1962), 417-453.
4. V. Arya and A. Banerjee, Strong backward uniqueness for sublinear parabolic equations, NoDEA Nonlinear Differential Equations Appl., 27 (2020), 18 pp.
5. L. Bakri.Carleman estimates for the Schrödinger operator. Applications to quantitative uniqueness, Comm. Partial Differential Equations, 38 (2013), 69-91.
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献