We study convergence properties of if , , , has a finite quasiconvex envelope, weakly in and for some it holds that as . In particular, we give necessary and sufficient conditions for -weak convergence of to if .
The vibration problem in two variables is derived from the spatial situation (a plate as a three-dimensional body) on the basis of geometrically nonlinear plate theory (using Kármán's hypothesis) and coupled linear thermoelasticity. That leads to coupled strongly nonlinear two-dimensional equilibrium and heat conducting equations (under classical mechanical and thermal boundary conditions). For the generalized problem with subgradient conditions on the boundary and in the domain (including also...
Let be an elliptic differential operator of second order with variable coefficients. In this paper it is proved that any -superharmonic function in the Riesz-Brelot sense is locally summable and satisfies the -superharmonicity in the sense of Schwartz distribution.