AbstractLower bounds for the real parts of the points in the spectrum of elliptic equationsdocumentclass{article}pagestyle{empty}begin{document}$$ begin{array}{l} Delta u + au_x + b{rm u}_{rm y} = - lambda u{rm in G} {rm u|}_{partial {rm G}} = 0 end{array} $$end{document}are derived. These bounds, depending only on the diameterLof the domainGand on the maximum normMof the coefficientsa, b, are optimal. They are always positive and thus the spectrum is bounded away from the imaginary axis. This result is then used to prove an “anti‐dynamo theorem” for magnetic fields with plane symmetry in the case of a compressible steady flow surrounded by a perfect cond
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