On the Correctness of Boundary Value Problems in the Mechanics of Continuous Media

Korn-Type Inequalities in Orlicz-Sobolev Spaces Involving the Trace-Free Part of the Symmetric Gradient and Applications to Regularity Theory

“…Many problems in mathematical theory of generalized Newtonian fluids and mechanics of solids lead to the following question (compare, for example, the monographs of Málek, Necǎs, Rokyta and Růžička [36], Duvaut and Lions [11] as well as Zeidler [47]): Is it possible to control a certain energy depending on ∇v by the corresponding one depending just on Ev, that is, doesˆΩ |∇v| p dx c(p, Ω)ˆΩ |Ev| p dx (1.2) hold for functions v ∈W 1,p (Ω; R n )? As shown by Gobert [27]- [28], Necǎs [38], Mosolov and Mjasnikov [35], Temam [45], and later by Fuchs [19] the inequality (1.1) is true for all 1 < p < ∞. (It should be emphasized that inequality (1.1) does not hold in case p = 1; see [39], or [9].)…”

A Posteriori Error Estimates for the Approximations of the Stresses in the Hencky Plasticity Problem

“…In our analysis we use a method suggested in [25] and also applied in [38]. where n = 2 n−1 −1 n−1 .…”

“…To this function we can apply an integral representation known as Cesaro's formula (see, for example, equation (13) in [25]): for x ∈ , y ∈ 0 it holds by letting z = S ,y x…”

Variational inequalities of Bingham type in three dimensions

“…For the proof of (1.1) we refer to Mosolov-Mjasnikov [12] and its bibliography. Combining (1.1) and the usual Sobolev inequality (see Berger [2]), we immediately obtain (1.2) for p, 1 < p < d. The inequality (1.2) with p = 1 has been proved by Strauss [16].…”