Eigenvalues and bifurcation for elliptic equations with mixed Dirichlet-Neumann boundary conditions related to Caffarelli-Kohn-Nirenberg inequalities - Colorado, Eduardo; Peral, Irened (Topological Methods in Nonlinear Analysis, 2004)
This work deals with the analysis ofeigenvalues, bifurcation and Hölder continuity of solutions tomixed problems like $$ \cases -\div (|x|^{-p\gamma} | abla u|^{p-2} abla u) = f_{\lambda}(x,u) ,&u > 0\ \text{ in }\Omega ,\\u = 0 &\text{ on }\Sigma_1,\\ |x|^{-p\gamma}| ablau|^{p-2}\dfrac{\partial u}{\partial u} = 0 &\text{ on } \Sigma_2,\endcases$$involving some potentials related with theCaffarelli-Kohn-Nirenberg inequalities, and with differentkind of functions $f_\lambda (x,u)$.