Abstract
This review is concerned with results obtained in a series of joint papers by V. Maz’ya and the author, and it covers a number of topics. First, explicit formulae for essential norms of the elastic and hydrodynamic double layer potentials are discussed for boundaries, having vertices and edges, and these norms are considered in the space of continuous vector-valued functions. Secondly, the explicit expressions for the best constants in estimates of solutions of some systems and equations of mathematical physics are surveyed. Third, criteria for the validity of the maximum modulus principle are stated for solutions of elliptic and parabolic systems. The fourth topic deals with necessary and sufficient conditions providing the maximum norm principle for parabolic systems. Here the norm is defined as Minkowski’ s functional of a convex body.
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