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Principle of symmetric criticality and evolution equations
1. | Department of Applied Physics, School of Science and Engineering, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo 169-8555, Japan |
2. | Department of Applied Physics, School of Science and Engineering, Waseda University, 3-4-1, Okubo, Tokyo, 169-8555 |
The purpose of this paper is to combine this result with the abstract theory developed in [1] and [2] concerning the evolution equation: $du(t)$/$dt + \partial\upsilon^1(u(t))- \partial\upsilon^2(u(t))$ ∋ $f(t)$ in V*, where $\partial\upsilon^i$ is the so-called subdifferential operator from a Banach space X into its dual V*. It is assumed that there exists a Hilbert space H satisfying $V \subset H \subset V $ and that G acts on these spaces as isometries. In this setting, the existence of G-symmetric solution for above equation can be discussed.
As an application, a parabolic problem with the p-Laplacian in unbounded domains is discussed.
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