Revisiting the sub- and super-solution method for the classical radial solutions of the mean curvature equation
| Autor: | Pierpaolo Omari, Franco Obersnel |
|---|---|
| Přispěvatelé: | Obersnel, Franco, Omari, Pierpaolo |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Robin
General Mathematics 01 natural sciences 35j62 Dirichlet distribution Dirichlet Neumann Robin periodic boundary condition sub- and super-solutions dirichlet classical solution symbols.namesake QA1-939 sub-solution 0101 mathematics periodic boundary conditions Geometry and topology Mathematics robin boundary conditions radial symmetry Mean curvature super-solution 010102 general mathematics Mathematical analysis Symmetry in biology 34c25 Robin boundary condition prescribed mean curvature equation 35j93 010101 applied mathematics 35j25 neumann symbols Dirichlet Neumann Robin periodic boundary conditions Super solution |
| Zdroj: | Open Mathematics, Vol 18, Iss 1, Pp 1185-1205 (2020) |
| ISSN: | 2391-5455 |
| Popis: | This paper focuses on the existence and the multiplicity of classical radially symmetric solutions of the mean curvature problem:−div∇v1+|∇v|2=f(x,v,∇v)inΩ,a0v+a1∂v∂ν=0on∂Ω,\left\{\begin{array}{ll}-\text{div}\left(\frac{\nabla v}{\sqrt{1+|\nabla v{|}^{2}}}\right)=f(x,v,\nabla v)& \text{in}\hspace{.5em}\text{Ω},\\ {a}_{0}v+{a}_{1}\tfrac{\partial v}{\partial \nu }=0& \text{on}\hspace{.5em}\partial \text{Ω},\end{array}\right.withΩ\text{Ω}an open ball inℝN{{\mathbb{R}}}^{N}, in the presence of one or more couples of sub- and super-solutions, satisfying or not satisfying the standard ordering condition. The novel assumptions introduced on the functionfallow us to complement or improve several results in the literature. |
| Databáze: | OpenAIRE |
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