Carleman estimates for sub-Laplacians on Carnot groups

Author:

Arya Vedansh,Kumar Dharmendra

Abstract

AbstractIn this note, we establish a new Carleman estimate with singular weights for the sub-Laplacian on a Carnot group $$\mathbb G$$ G for functions satisfying the discrepancy assumption in (2.16) below. We use such an estimate to derive a sharp vanishing order estimate for solutions to stationary Schrödinger equations.

Funder

University of Jyväskylä

Publisher

Springer Science and Business Media LLC

Subject

Mathematical Physics,Algebra and Number Theory,Analysis

Reference29 articles.

1. Almgren, F.: Dirichlet’s problem for multiple valued functions and the regularity of mass minimizing integral currents. In: Minimal Submanifolds and Geodesics (Proc. Japan-United States Sem., Tokyo, 1977), pp. 1-6. North-Holland, Amsterdam (1979)

2. Aronszajn, N.: A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order. J. Math. Pures Appl. (9) 36, 235–249 (1957)

3. Aronszajn, N., Krzywicki, A., Szarski, J.: A unique continuation theorem for exterior differential forms on Riemannian manifolds. Ark. Mat. 4(1962), 417–453 (1962)

4. Bahouri, H.: Non prolongement unique des solutions d’opérateurs “somme de carrés” (French) [Failure of unique continuation for “sum of squares” operators]. Ann. Inst. Fourier (Grenoble) 36, 137–155 (1986)

5. Bakri, L.: Quantitative uniqueness for Schrödinger operator. Indiana Univ. Math. J. 61(4), 1565–1580 (2012)

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