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The Maximum Principle and the Moving Plane Method

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Abstract

In this article we discuss the maximum principle and it’s application to the study of symmetry of solutions of nonlinear partial differential equations, which was one of the main research topics of Louis Nirenberg. The central question in symmetry that we discuss is the following if a domain Ω ⊂ ℝN and the given boundary data on ∂Ω have some symmetry, for example radial symmetry, axial symmetry or symmetry with respect to some hyperplane, then when we can say that positive solution of a given nonlinear partial differential equation on Ω inherit these symmetries.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Science Education and Research, Dr Homi Bhabha Road, Pune, 411 008, India

    Mousomi Bhakta

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  1. Mousomi Bhakta
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Correspondence to Mousomi Bhakta.

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The author is currently an Associate Professor in IISER-Pune. She completed her PhD from TIFR-CAM, Bangalore in 2011. After holding postdoc position in Technion, Israel for two years and UNE, Australia for one year, she joined as an Assistant Professor in IISER-Pune in 2014. She has received INSA Young Scientist award in Mathematics in 2018.

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Bhakta, M. The Maximum Principle and the Moving Plane Method. Reson 25, 757–763 (2020). https://doi.org/10.1007/s12045-020-0994-y

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  • DOI: https://doi.org/10.1007/s12045-020-0994-y

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