Existence and uniqueness of solutions for some degenerate nonlinear elliptic equations

Albo Carlos Cavalheiro

Archivum Mathematicum (2014)

  • Volume: 050, Issue: 1, page 51-63
  • ISSN: 0044-8753

Abstract

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In this article we are interested in the existence and uniqueness of solutions for the Dirichlet problem associated with the degenerate nonlinear elliptic equations Δ ( v ( x ) | Δ u | p - 2 Δ u ) - ∑ j = 1 n D j [ ω ( x ) 𝒜 j ( x , u , ∇ u ) ] = f 0 ( x ) - ∑ j = 1 n D j f j ( x ) , i n Ω in the setting of the weighted Sobolev spaces.

How to cite

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Cavalheiro, Albo Carlos. "Existence and uniqueness of solutions for some degenerate nonlinear elliptic equations." Archivum Mathematicum 050.1 (2014): 51-63. <http://eudml.org/doc/261061>.

@article{Cavalheiro2014,
abstract = {In this article we are interested in the existence and uniqueness of solutions for the Dirichlet problem associated with the degenerate nonlinear elliptic equations \begin\{align*\}\{\Delta \}(v(x)\, \{\vert \{\Delta \}u\vert \}^\{p-2\}\{\Delta \}u) &-\sum \_\{j=1\}^n D\_j\{\bigl [\}\{\omega \}(x) \{\mathcal \{A\}\}\_j(x, u, \{\nabla \}u)\{\bigr ]\}\\ =&\ f\_0(x) - \sum \_\{j=1\}^nD\_jf\_j(x)\,, \quad \mbox \{in\}\quad \{\Omega \}\end\{align*\} in the setting of the weighted Sobolev spaces.},
author = {Cavalheiro, Albo Carlos},
journal = {Archivum Mathematicum},
keywords = {degenerate nolinear elliptic equations; weighted Sobolev spaces; degenerate nolinear elliptic equations; weighted Sobolev spaces},
language = {eng},
number = {1},
pages = {51-63},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Existence and uniqueness of solutions for some degenerate nonlinear elliptic equations},
url = {http://eudml.org/doc/261061},
volume = {050},
year = {2014},
}

TY - JOUR
AU - Cavalheiro, Albo Carlos
TI - Existence and uniqueness of solutions for some degenerate nonlinear elliptic equations
JO - Archivum Mathematicum
PY - 2014
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 050
IS - 1
SP - 51
EP - 63
AB - In this article we are interested in the existence and uniqueness of solutions for the Dirichlet problem associated with the degenerate nonlinear elliptic equations \begin{align*}{\Delta }(v(x)\, {\vert {\Delta }u\vert }^{p-2}{\Delta }u) &-\sum _{j=1}^n D_j{\bigl [}{\omega }(x) {\mathcal {A}}_j(x, u, {\nabla }u){\bigr ]}\\ =&\ f_0(x) - \sum _{j=1}^nD_jf_j(x)\,, \quad \mbox {in}\quad {\Omega }\end{align*} in the setting of the weighted Sobolev spaces.
LA - eng
KW - degenerate nolinear elliptic equations; weighted Sobolev spaces; degenerate nolinear elliptic equations; weighted Sobolev spaces
UR - http://eudml.org/doc/261061
ER -

References

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