Opuscula Mathematica
Opuscula Math. 29, no. 4 (), 377-391
Opuscula Mathematica

On elliptic problems with a nonlinearity depending on the gradient

Abstract. We investigate the solvability of the Neumann problem \((1.1)\) involving the nonlinearity depending on the gradient. We prove the existence of a solution when the right hand side \(f\) of the equation belongs to \(L^m(\Omega )\) with \(1 \leq m \lt 2\).
Keywords: Neumann problem, nonlinearity depending on the gradient, \(L^1\) data.
Mathematics Subject Classification: 35D05, 35J25, 35J60.
Cite this article as:
Jan Chabrowski, On elliptic problems with a nonlinearity depending on the gradient, Opuscula Math. 29, no. 4 (2009), 377-391, http://dx.doi.org/10.7494/OpMath.2009.29.4.377
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.