In this paper we give a survey of selected results and open problems on integral inequalities of Mathematical Physics connected with the papers of V. Maz’ya, S. Fillippas, A. Tertikas, R. Osserman, A. Ancona, H. Brezis, M. Marcus, Y. Pinchover, E. B. Davies, A. Laptev, J. L. Fernández, J. M. Rodríguez, P. Caldiroli, R. Musina, A. A. Balinsky, W. D. Evans, R. T. Lewis, R. G. Nasibullin, I. K. Shafigullin, the author and other mathematicians. In addition, we give some new examples and present non-linear relationships between global numerical characteristics of domains in the Euclidean space of dimension \(n\ge 2\).

在本文中，我们对与 V. Maz'ya、S. Fillippas、A. Tertikas、R. Osserman、A. Ancona、H. Brezis、 M. Marcus、Y. Pinchover、EB Davies、A. Laptev、JL Fernández、JM Rodríguez、P. Caldiroli、R. Musina、AA Balinsky、WD Evans、RT Lewis、RG Nasibullin、IK Shafigullin、作者和其他数学家。此外，我们给出了一些新的例子，并展示了维度为\(n\ge 2\)的欧几里德空间中域的全局数值特征之间的非线性关系。