Existence of solutions for Navier problems with degenerate nonlinear elliptic equations

Albo Carlos Cavalheiro

Communications in Mathematics (2015)

  • Volume: 23, Issue: 1, page 33-45
  • ISSN: 1804-1388

Abstract

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In this paper we are interested in the existence and uniqueness of solutions for the Navier problem associated to the degenerate nonlinear elliptic equations Δ ( v ( x ) | Δ u | q - 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 ) , in Ω in the setting of the weighted Sobolev spaces.

How to cite

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Cavalheiro, Albo Carlos. "Existence of solutions for Navier problems with degenerate nonlinear elliptic equations." Communications in Mathematics 23.1 (2015): 33-45. <http://eudml.org/doc/271642>.

@article{Cavalheiro2015,
abstract = {In this paper we are interested in the existence and uniqueness of solutions for the Navier problem associated to the degenerate nonlinear elliptic equations \begin\{equation*\} \Delta (v(x)\,\vert \Delta u\vert ^\{q-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), \text\{ in \}\Omega \end\{equation*\} in the setting of the weighted Sobolev spaces.},
author = {Cavalheiro, Albo Carlos},
journal = {Communications in Mathematics},
keywords = {degenerate nolinear elliptic equations; weighted Sobolev spaces; Navier problem},
language = {eng},
number = {1},
pages = {33-45},
publisher = {University of Ostrava},
title = {Existence of solutions for Navier problems with degenerate nonlinear elliptic equations},
url = {http://eudml.org/doc/271642},
volume = {23},
year = {2015},
}

TY - JOUR
AU - Cavalheiro, Albo Carlos
TI - Existence of solutions for Navier problems with degenerate nonlinear elliptic equations
JO - Communications in Mathematics
PY - 2015
PB - University of Ostrava
VL - 23
IS - 1
SP - 33
EP - 45
AB - In this paper we are interested in the existence and uniqueness of solutions for the Navier problem associated to the degenerate nonlinear elliptic equations \begin{equation*} \Delta (v(x)\,\vert \Delta u\vert ^{q-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), \text{ in }\Omega \end{equation*} in the setting of the weighted Sobolev spaces.
LA - eng
KW - degenerate nolinear elliptic equations; weighted Sobolev spaces; Navier problem
UR - http://eudml.org/doc/271642
ER -

References

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  2. Cavalheiro, A.C., 10.7494/OpMath.2013.33.3.439, Opuscula Math., 33, 3, 2013, 439-453, (2013) MR3046406DOI10.7494/OpMath.2013.33.3.439
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