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Symmetry, maximum principle, nonlinear equations.

In this article we discuss the maximum principle and it’s ap-plication to the study of symmetry of solutions of nonlinear partial differential equations, which was one of the main re-search 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 posi-tive solution of a given nonlinear partial differential equation on Ω inherit these symmetries.

Mousomi Bhakta¹

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

Published

4 June 2020