ON THE MINIMAL ENERGY SOLUTION IN A QUASILINEAR ELLIPTIC EQUATION

Title & Authors
ON THE MINIMAL ENERGY SOLUTION IN A QUASILINEAR ELLIPTIC EQUATION
Park, Sang-Don; Kang, Chul;

Abstract
In this paper we seek a positive, radially symmetric and energy minimizing solution of an m-Laplacian equation, -div$($\small{\mid}${\nabla}u$\small{\mid}$^{m-2}$\small{\mid}${\nabla}u)\;=\;h(u)$. In the variational sense, the solutions are the critical points of the associated functional called the energy, $J(v)\;=\;\frac{1}{m}\;\int_{R^N}\;$\small{\mid}${\nabla}v$\small{\mid}$^m\;-\;\int_{R^N}\;H(v)dx,\;where\;H(v)\;=\;{\int_0}^v\;h(t)dt$. A positive, radially symmetric critical point of J can be obtained by solving the constrained minimization problem; minimize{$\int_{R^N}$\small{\mid}${\nabla}u$\small{\mid}$^mdx$\small{\mid}$\;\int_{R^N}\;H(u)d;=\;1$}. Moreover, the solution minimizes J(v).
Keywords
quasilinear elliptic;m-Laplacian;constrained minimization;variational equation;radially symmetric;Lagrange multiplier;
Language
English
Cited by
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