New estimates for div-curl products and very weak solutions of PDEs
Carlo Sbordone (1997)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Displaying similar documents to “Liouville type theorems for φ-subharmonic functions.”
New estimates for div-curl products and very weak solutions of PDEs
Improved estimates for the Ginzburg-Landau equation : the elliptic case
Fabrice Bethuel, Giandomenico Orlandi, Didier Smets (2005)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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We derive estimates for various quantities which are of interest in the analysis of the Ginzburg-Landau equation, and which we bound in terms of the -energy and the parameter . These estimates are local in nature, and in particular independent of any boundary condition. Most of them improve and extend earlier results on the subject.
A value-distribution criterion for the class and some related questions
M. Essen, D. F. Shea, C. S. Stanton (1985)
Annales de l'institut Fourier
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We give a necessary and sufficient condition for an analytic function in to have real part in class . This condition contains the classical one of Zygmund; other variants are also given.
Quasiharmonic fields
Tadeusz Iwaniec, Carlo Sbordone (2001)
Annales de l'I.H.P. Analyse non linéaire
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Estimates of the first eigenvalue of a big cup domain of a 2-sphere
Tadayuki Matsuzawa, Shukichi Tanno (1982)
Compositio Mathematica
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Multi-bump ground states of the Gierer–Meinhardt system in R2
Manuel del Pino, Michał Kowalczyk, Juncheng Wei (2003)
Annales de l'I.H.P. Analyse non linéaire
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Superharmonicity of nonlinear ground states.
Peter Lindqvist, Juan Manfredi, Eero Saksman (2000)
Revista Matemática Iberoamericana
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The objective of our note is to prove that, at least for a convex domain, the ground state of the p-Laplacian operator Δpu = div (|∇u|p-2 ∇u) is a superharmonic function, provided that 2 ≤ p ≤ ∞. The ground state of Δp is the positive solution with boundary values zero of the equation div(|∇u|p-2 ∇u) + λ |u|p-2 u = 0 in the bounded domain...