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arXiv · 1804.03712

Weighted gradient inequalities and unique continuation problems

laura De Carli·Dmitry Gorbachev·Sergey Tikhonov
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Abstract

We use Pitt inequalities for the Fourier transform to prove the following weighted gradient inequality $$ \|e^{-\tau\ell(\cdot)} u^{\frac 1q} f\|_q\leq c_\tau\| e^{-\tau\ell(\cdot)} v^{\frac 1p}\, \nabla f\|_p, \quad f\in C^\infty_0( R^n). $$ This inequality is a Carleman-type estimate that yields unique continuation results for solutions of first order differential equations and systems.

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laura De Carli, Dmitry Gorbachev, Sergey Tikhonov. 2018-04-10. Weighted gradient inequalities and unique continuation problems. https://arxiv.org/abs/1804.03712

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