arXiv:1708.01899 Abstract | arXiv Analytics

arXiv:1708.01899 [math.AP]Abstract References Reviews Resources

Quantitative uniqueness of solutions to parabolic equations

Published 2017-08-06Version 1

We investigate the quantitative uniqueness of solutions to parabolic equations with lower order terms on compact smooth manifolds. Quantitative uniqueness is a quantitative form of strong unique continuation property. We characterize quantitative uniqueness by the rate of vanishing. We can obtain the vanishing order of solutions by $C^{1, 1}$ norm of the potential functions, as well as the $L^\infty$ norm of the coefficient functions. Some quantitative Carleman estimates and three cylinder inequalities are established.

Comments: 23 pages

Categories: math.AP

Keywords: quantitative uniqueness, parabolic equations, strong unique continuation property, compact smooth manifolds, lower order terms

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