Quantitative uniqueness of solutions to parabolic equations
Abstract
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 C1, 1 norm of the potential functions, as well as the L∞ norm of the coefficient functions. Some quantitative Carleman estimates and three cylinder inequalities are established.
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