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

Eduardo Colorado, Irened Peral

DOI: http://dx.doi.org/10.12775/TMNA.2004.011

Abstract


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

Keywords


Equivalence problems; bifurcation; mixed boundary conditions; Cafarelli-Kohn-Nihrenberg inequalities

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