  Sharp lower and upper uniform estimates are obtained for fundamental
frequencies of $p$-Laplace type operators generated by quadratic forms. Optimal
constants are exhibited, rigidity of the upper estimate is proved, anisotropic
attainability of the lower estimate is derived as well as characterization of
anisotropic extremizers for circular and rectangular membranes. Sharp
quantitative anisotropic inequalities associated with lower constants are also
established, providing as a by-product information on anisotropic stability.
When the uniform ellipticity condition is relaxed, we show that the optimal
lower constant remains positive, while anisotropic extremizers no longer exist.
Our sharp lower estimate can be viewed as an isoanisotropic counterpart of the
Faber-Krahn isoperimetric inequality in the plane.
