caa a22 4500 445843403 CHVBK 20180317145351.0 cr unu---uuuuu 170323e20110501xx s 000 0 eng 10.1007/s00526-010-0358-7 doi (NATIONALLICENCE)springer-10.1007/s00526-010-0358-7 Liu Dan Department of Mathematics, East China Normal University, 200062, Shanghai, People's Republic of China aut Hausdorff measure of critical sets of solutions to magnetic schrödinger equations [Elektronische Daten] [Dan Liu] In this paper, we study the critical set of a complex-valued solution to a Schrödinger equation involving the magnetic field and with a nonlinear term, where the critical set is $${\{x\in\Omega:~\psi(x)=0, ~\nabla\psi(x)=0\}}$$ . We consider this equation in a bounded domain of $${\mathbb{R}^3}$$ with the boundary condition: $${\nabla _{\mathbf{A}}\psi\cdot \nu=0}$$ , and we establish a global 1-dimensional Hausdorff measure estimate for the critical sets. From the proof of global estimates, we find that our methods work as well for more general equations with a magnetic potential. Springer-Verlag, 2010 Calculus of Variations and Partial Differential Equations Springer-Verlag 41/1-2(2011-05-01), 179-202 0944-2669 41:1-2<179 2011 41 526 https://doi.org/10.1007/s00526-010-0358-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00526-010-0358-7 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Liu Dan Department of Mathematics, East China Normal University, 200062, Shanghai, People's Republic of China aut NATIONALLICENCE 773 0- Calculus of Variations and Partial Differential Equations Springer-Verlag 41/1-2(2011-05-01), 179-202 0944-2669 41:1-2<179 2011 41 526 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer