Geodesic
Nonlinear Neumann problems on bounded Lipschitz domains
Electronic Journal of Differential Equations, Tome 2005 (2005).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We prove existence and uniqueness, up to a constant, of an entropy solution to the nonlinear and non homogeneous Neumann problem $$\displaylines{ -\mathop{\rm div}[ \mathbf{a}(.,\nabla u)] +\beta (u)=f \quad\hbox{ in } \Omega \cr \frac{\partial u}{\partial \nu _{\mathbf{a}}}+\gamma (\tau u)=g \quad \hbox{on } \partial \Omega\,. }$$ Our approach is based essentially on the theory of m-accretive operators in Banach spaces, and in order preserving properties.
Classification : 35J60, 35J70, 47J05
Keywords: nonlinear Neumann problem, m-completely accretive operator 
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     author = {Siai, Abdelmajid},
     title = {Nonlinear {Neumann} problems on bounded {Lipschitz} domains},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2005},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a43/}
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Siai, Abdelmajid. Nonlinear Neumann problems on bounded Lipschitz domains. Electronic Journal of Differential Equations, Tome 2005 (2005). http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a43/