Geodesic
On the Neumann Problem for the Schrödinger Equations with Singular Potentials in Lipschitz Domains
Canadian journal of mathematics, Tome 56 (2004) no. 3, pp. 655-672

Voir la notice de l'article provenant de la source Cambridge University Press

We consider the Neumann problem for the Schrödinger equations $-\Delta u\,+\,Vu\,=\,0$ , with singular nonnegative potentials $V$ belonging to the reverse Hölder class ${{\mathcal{B}}_{n}}$ , in a connected Lipschitz domain $\Omega \,\subset \,{{\text{R}}^{n}}$ . Given boundary data $g$ in ${{H}^{p}}\text{or}\,{{L}^{p}}\,\text{for}\,\text{1}-\in \,<\,p\,\le \,2,\text{where}\,\text{0}<\in <\frac{1}{n}$ , it is shown that there is a unique solution, $u$ , that solves the Neumann problem for the given data and such that the nontangential maximal function of $\nabla u$ is in ${{L}^{p}}(\partial \Omega )$ . Moreover, the uniform estimates are found.
DOI : 10.4153/CJM-2004-030-9
Mots-clés : 42B20, 35J10, Neumann problem, Schrödinger equation, Lipschitz domain, reverse Hölder class, Hp space 
Tao, Xiangxing; Wang, Henggeng. On the Neumann Problem for the Schrödinger Equations with Singular Potentials in Lipschitz Domains. Canadian journal of mathematics, Tome 56 (2004) no. 3, pp. 655-672. doi: 10.4153/CJM-2004-030-9
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