Stone-regularity conjecture for boundary-value problems with polynomial resolvent growth

Let a boundary-value problem be subject to the estimate referenced in the source as

, with smooth coefficients $p_k$. A boundary-value problem is **Stone-regular** when it has the corresponding Stone-regularity property. **Stone-regularity conjecture.** Every such boundary-value problem is Stone-regular. Moreover, this assertion should also hold for general boundary conditions

. The conjecture proposes a general regularity consequence of polynomial resolvent growth, extending the expected conclusion from smooth-coefficient problems to general boundary conditions; the source does not state a resolution.