A Variational Inequality for a Degenerate Elliptic Operator Under Minimal Assumptions on the Coefficients

Vitanza, Carmela ; Zamboni, Pietro

Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 2, pp. 341-356

Résumé

In this note we obtain the existence and the uniqueness of the solution of a variational inequality associated to the degenerate operator \begin{equation*}\tag{*} Lu = - \sum^n_{i,j=1} (a_{ij}(x)u_{x_i} + d_j u)_{x_j} + \sum^n_{i=1} b_i u_{x_i} + cu\end{equation*} assuming the coefficients of the lower terms and the known term belonging to a suitable degenerate Stummel-Kato class. The weight $w$, which gives the degeneration, belongs to the Muckenoupt class $A^2$.