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Asymptotic symmetry of solutions of nonlinear partial differential equations
Author(s) -
Badiale Marino,
Bardi Martino
Publication year - 1992
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160450705
Subject(s) - mathematics , degenerate energy levels , infinity , symmetry (geometry) , mathematical analysis , nonlinear system , partial differential equation , elliptic partial differential equation , limit (mathematics) , class (philosophy) , numerical partial differential equations , asymptotic analysis , physics , geometry , quantum mechanics , artificial intelligence , computer science
For a large class of partial differential equations on exterior domains or on ℝ N we show that any solution tending to a limit from one side as x goes to infinity satisfies the property of “asymptotic spherical symmetry”. The main examples are semilinear elliptic equations, quasilinear degenerate elliptic equations, and first‐order Hamilton‐Jacobi equations.