De Giorgi type results for elliptic systems
نویسندگان
چکیده
منابع مشابه
The De Giorgi Conjecture on Elliptic Regularization
The statement of Conjecture 1.1 does not specify the convergence notion for u → u nor the solution notion for equation (1.1). We shall tacitly assume in the following that the convergence is (at least) almost everywhere in space and time, that convergence holds (at least) for subsequences, and that equation (1.1) will be solved (at least) in the distributional sense. Along with these provisions...
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In 1978 De Giorgi formulated the following conjecture. Let u be a solution of ∆u = u − u in all of R such that |u| ≤ 1 and ∂xnu > 0 in R. Is it true that all level sets {u = λ} of u are hyperplanes, at least if n ≤ 8? Equivalently, does u depend only on one variable? When n = 2, this conjecture was proved in 1997 by N. Ghoussoub and C. Gui. More recently, L. Ambrosio and the author have proved ...
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ژورنال
عنوان ژورنال: Calculus of Variations and Partial Differential Equations
سال: 2012
ISSN: 0944-2669,1432-0835
DOI: 10.1007/s00526-012-0536-x