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Zbl 0772.35008
Ruiz, A.; Vega, L.
Unique continuation for the solutions of the Laplacian plus a drift. (English)
[J] Ann. Inst. Fourier 41, No.3, 651-663 (1991). ISSN 0373-0956; ISSN 1777-5310/e

Summary: We prove unique continuation for solutions of the inequality $\vert\Delta u(x)\vert\le V(x)\vert\nabla u(x)\vert$, $x\in\Omega$ a connected set contained in $\bbfR\sp n$ and $V$ is in the Morrey spaces $F\sp{\alpha,p}$, with $p\ge(n-2)/2(1-\alpha)$ and $\alpha<1$. These spaces include $L\sp q$ for $q\ge(3n-2)/2$ [voir {\it L. Hörmander}, Commun. Partial Differ. Equations 8, 21-64 (1983; Zbl 0546.35023); {\it B. Barcelo}, {\it C. E. Kenig}, {\it A. Rutz} and {\it C. D. Sogge}, Ill. J. Math. 32, No. 2, 230-245 (1988; Zbl 0689.35015)]. If $p=(n-2)/2(1- \alpha)$, the extra assumption of $V$ being small enough is needed.

MSC 2000:: *35B60 Continuation of solutions of PDE
35L15 Second order hyperbolic equations, initial value problems
42B25 Maximal functions

Keywords: Carleman $L(\sup 2)$-weighted inequalities; diadic decomposition; Morrey spaces

Citations: Zbl 0546.35023; Zbl 0689.35015

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