Topological Methods in Nonlinear Analysis

Eigenvalues and bifurcation for elliptic equations with mixed Dirichlet-Neumann boundary conditions related to Caffarelli-Kohn-Nirenberg inequalities

Eduardo Colorado and Irened Peral

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Abstract

This work deals with the analysis of eigenvalues, bifurcation and Hölder continuity of solutions to mixed problems like $$ \begin{cases} -{\rm div} (|x|^{-p\gamma} |\nabla u|^{p-2}\nabla u) = f_{\lambda}(x,u) , &u > 0\ \text{ in }\Omega ,\\ u = 0 &\text{ on }\Sigma_1,\\ |x|^{-p\gamma}|\nabla u|^{p-2}\dfrac{\partial u}{\partial \nu} = 0 &\text{ on } \Sigma_2, \end{cases} $$ involving some potentials related with the Caffarelli-Kohn-Nirenberg inequalities, and with different kind of functions $f_\lambda (x,u)$.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 23, Number 2 (2004), 239-273.

Dates
First available in Project Euclid: 31 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1464731409

Mathematical Reviews number (MathSciNet)
MR2078192

Zentralblatt MATH identifier
1075.35014

Citation

Colorado, Eduardo; Peral, Irened. Eigenvalues and bifurcation for elliptic equations with mixed Dirichlet-Neumann boundary conditions related to Caffarelli-Kohn-Nirenberg inequalities. Topol. Methods Nonlinear Anal. 23 (2004), no. 2, 239--273. https://projecteuclid.org/euclid.tmna/1464731409


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