estimates for solutions to non-uniformly elliptic PDE'S with measurable coefficients.
Wave equations with low regularity coefficients.
Well-Posedness of a Semilinear Heat Equation with Weak Initial Data.
Worst scenario method in homogenization. Linear case
The paper deals with homogenization of a linear elliptic boundary problem with a specific class of uncertain coefficients describing composite materials with periodic structure. Instead of stochastic approach to the problem, we use the worst scenario method due to Hlaváček (method of reliable solution). A few criterion functionals are introduced. We focus on the range of the homogenized coefficients from knowledge of the ranges of individual components in the composite, on the values of generalized...