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Symmetry properties of the solutions to Thomas-Fermi-Dirac-von Weizsäcker type equations

Authors: Rafael D. Benguria and Cecilia Yarur
Journal: Trans. Amer. Math. Soc. 320 (1990), 665-675
MSC: Primary 35J60; Secondary 35A30, 35Q20, 81C05
MathSciNet review: 974511
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Abstract: We consider a semilinear elliptic equation with a spherically symmetric potential (specifically, Thomas-Fermi-Dirac-von Weizsäcker type equations without electronic repulsion). Assuming some regularity properties of the solutions at the origin and at infinity, we prove that the solutions have spherical symmetry.

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Keywords: Semilinear elliptic equations, Thomas-Fermi-Dirac-von Weizsäcker equations, uniqueness of positive solutions, spherical symmetry of solutions
Article copyright: © Copyright 1990 American Mathematical Society