Boundedness of the gradient of a solution for the fourth order equation in general domains

Based on new integral estimate, we establish boundedness of the gradient of a solution for a fourth order equation in an arbitrary three-dimensional domain

Interplay between Quantum Size Effect and Strain Effect on Growth of Nanoscale Metal Thin Film

We develop a theoretical framework to investigate the interplay between quantum size effect (QSE) and strain effect on the stability of metal nanofilms. The QSE and strain effect are shown to be coupled through the concept of "quantum electronic stress. First-principles calculations reveal large quantum oscillations in the surface stress of metal nanofilms as a function of film thickness. This adds extrinsically additional strain-coupled quantum oscillations to surface energy of strained metal nanofilms. Our theory enables a quantitative estimation of the amount of strain in experimental samples, and suggests strain be an important factor contributing to the discrepancies between the existing theories and experiments