Opuscula Mathematica
Opuscula Math. 34, no. 1 (), 15-28
http://dx.doi.org/10.7494/OpMath.2014.34.1.15
Opuscula Mathematica

Existence and uniqueness of the solutions of some degenerate nonlinear elliptic equations


Abstract. In this paper we are interested in the existence of solutions for the Dirichlet problem associated with degenerate nonlinear elliptic equations \[\begin{split}&-\sum_{j=1}^n D_j{\bigl[}{\omega}(x) {\cal A}_j(x, u, {\nabla}u){\bigr]} + b(x, u, {\nabla}u)\,{\omega}(x) + g(x)\,u(x)=\\&= f_0(x) - \sum_{j=1}^nD_jf_j(x) \quad{\rm on}\quad {\Omega}\end{split}\] in the setting of the weighted Sobolev spaces \({\rm W}_0^{1,p}(\Omega, \omega)\).
Keywords: degenerate nonlinear elliptic equations, weighted Sobolev spaces.
Mathematics Subject Classification: 35J70, 35J60.
Cite this article as:
Albo Carlos Cavalheiro, Existence and uniqueness of the solutions of some degenerate nonlinear elliptic equations, Opuscula Math. 34, no. 1 (2014), 15-28, http://dx.doi.org/10.7494/OpMath.2014.34.1.15
 
Download this article's citation as:
a .bib file (BibTeX), a .ris file (RefMan), a .enw file (EndNote)
or export to RefWorks.

RSS Feed

horizontal rule

ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
Copyright © 2003−2017 OPUSCULA MATHEMATICA
Contact: opuscula@agh.edu.pl
Made by Tomasz Zabawa

horizontal rule

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.