Lower bounds at infinity for solutions to second order elliptic equations
DOI:
https://doi.org/10.58997/ejde.2023.69Keywords:
Carleman estimates; strong unique continuationAbstract
We study lower bounds at infinity for solutions to $$ |Pu|\leq M|x|^{-\delta_1}|\nabla u|+M|x|^{-\delta_{0}}|u| $$ where $P$ is a second order elliptic operator. Our results are of quantitative nature and generalize those obtained in [3,6].
For more information see https://ejde.math.txstate.edu/Volumes/2023/69/abstr.html
References
J. Bourgain, C. E. Kenig; On localization in the continuous Anderson-Bernoulli model in higher dimension. Invent. Math., 161(2):389-426, 2005.
J. Cruz-Sampedro; Unique continuation at infinity of solutions to schršodinger equations with complex-valued potentials. Proc. Edinburgh Math. Soc. (2), 42(1):143-153, 1999.
B. Davey; Some quantitative unique continuation results for eigenfunctions of the magnetic schršodinger operator. Comm. Partial Differential Equations, 39(5):876-945, 2014.
L. Escauriaza, S. Vessella; Optimal three cylinder inequalities for solutions to parabolic equations with lipschitz leading coefficients. Comtemp. Math., 333:79-87, 2003.
L. Homander; Uniqueness theorems for second order elliptic differential equations. Comm. P.D.E., 8:21-64, 1983.
C.-L. Lin, J.-N. Wang; Quantitative uniqueness estimates for the general second order elliptic equations. J. Funct. Anal., 266(8):5108-5125, 2014.
V. Z. Meshkov; On the possible rate of decay at infinity of solutions of second order partial differential equations. Matematicheskii Sbornik, 182(3):364-383, 1991.
Downloads
Published
License
Copyright (c) 2023 Tu Nguyen
This work is licensed under a Creative Commons Attribution 4.0 International License.
