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


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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
Sprache:
Englisch
Zeitrahmen der Veröffentlichung:
2 Hefte pro Jahr
Fachgebiete der Zeitschrift:
Mathematik, Allgemeines