elliptic equations maximum principle eigenvalue problem
Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences
The maximum principle for linear second-order elliptic equations in divergence form is investigated. By means of new formulas for the first eigenvalue necessary and sufficient conditions for the validity of the maximum principle are obtained. Some qualitative properties of the first eigenvalue with respect to the coefficients of the equation are proved. AMS subject classification: 35J15, 35B50, 35B05, 35J25.