We derive some 1-D symmetry and uniqueness or non-existence results for nonnegative solutions of {-div(A(x)∇;u)=u-g(x)inR+Nu=0on}R+N in low dimension, under suitable assumptions on A and g. Our method is based upon a combination of Fourier series and Liouville theorems. © 2013 Elsevier Ltd.
Farina, A., Soave, N. (2013). Symmetry and uniqueness of nonnegative solutions of some problems in the halfspace. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 403(1), 215-233 [10.1016/j.jmaa.2013.02.048].
Symmetry and uniqueness of nonnegative solutions of some problems in the halfspace
SOAVE, NICOLA
2013
Abstract
We derive some 1-D symmetry and uniqueness or non-existence results for nonnegative solutions of {-div(A(x)∇;u)=u-g(x)inR+Nu=0on}R+N in low dimension, under suitable assumptions on A and g. Our method is based upon a combination of Fourier series and Liouville theorems. © 2013 Elsevier Ltd.
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