Acceso abierto

Existence and uniqueness of solution for a class of nonlinear degenerate elliptic equation in weighted Sobolev spaces


Cite

In this work we are interested in the existence and uniqueness of solutions for the Navier problem associated to the degenerate nonlinear elliptic equations Δ(v(x)|Δu|r2Δu)j=1nDj[w1(x)𝒜j(x,u,u)]+b(x,u,u)w2(x)=f0(x)j=1nDjfj(x),inΩ$$\matrix{{\Delta {\rm{(v}}({\rm{x}})\left| {\Delta {\rm{u}}} \right|^{{\rm{r}} - 2} \Delta {\rm{u}}) - \sum\limits_{{\rm{j}} = 1}^{\rm{n}} {{\rm{D}}_{\rm{j}} [{\rm{w}}_1 ({\rm{x}}){\cal{A}}_{\rm{j}} ({\rm{x}},{\rm{u}},\nabla {\rm{u}})]} } \hfill \cr { + \;{\rm{b}}({\rm{x}},{\rm{u}},\nabla {\rm{u}})\;{\rm{w}}_2 ({\rm{x}}) = {\rm{f}}_0 ({\rm{x}}) - \sum\limits_{{\rm{j}} = 1}^{\rm{n}} {{\rm{D}}_{\rm{j}} {\rm{f}}_{\rm{j}} ({\rm{x}}),\;\;\;\;\;{\rm{in}}\;\Omega } }}$$ in the setting of the Weighted Sobolev Spaces.

eISSN:
2066-7752
Idioma:
Inglés
Calendario de la edición:
2 veces al año
Temas de la revista:
Mathematics, General Mathematics