Addition to the Fichera paper
Theorems of the Liouville type for elliptic systems of partial differential equations
Si considerano sistemi ellittici generali di equazioni alle derivate parziali e per essi si stabiliscono teoremi analoghi a quello classico di Liouville sulle funzioni armoniche, poggiando su di una proposizione relativa all'analiticità delle soluzioni di certe equazioni ellittiche. Alcuni teoremi del tipo di quelli qui ottenuti trovansi già in [1].
On asymptotics of solutions and eigenvalues of the boundary value problem with rapidly alternating boundary conditions for the system of elasticity
Boundary value problems for the system of linear elasticity with rapidly alternating boundary conditions are studied and asymptotic behavior of solutions is considered when a small parameter, which defines the oscillation of the boundary conditions, tends to zero. Estimates for the difference between such solutions and solutions of the limit problem are given.
On homogeneizatìon problems for the Laplace operator in partially perforated domains with Neumann's condition on the boundary of cavities.
In this paper the problem of homogeneization for the Laplace operator in partially perforated domains with small cavities and the Neumann boundary conditions on the boundary of cavities is studied. The corresponding spectral problem is also considered.
Estimates near the boundary for second order derivatives of solutions of the Dirichlet problem for the biharmonic equation
Per ogni soluzione della (1) nel dominio limitato ,, appartenente a e soddisfacente le condizioni (2), si dimostra la maggiorazione (5), valida nell'intorno di ogni punto del contorno; si consente a di essere singolare in .
On the homogenization of the Poisson equation in partially perforated domains with arbitrary density of cavities and mixed type conditions on their boundary
In this paper we study the behavior of solutions of the boundary value problem for the Poisson equation in a partially perforated domain with arbitrary density of cavities and mixed type conditions on their boundary. The corresponding spectral problem is also considered. A short communication of similar results can be found in [1].
Estimates near the boundary for second order derivatives of solutions of the Dirichlet problem for the biharmonic equation
Per ogni soluzione della (1) nel dominio limitato ,, appartenente a e soddisfacente le condizioni (2), si dimostra la maggiorazione (5), valida nell'intorno di ogni punto del contorno; si consente a di essere singolare in .
Homogenization of differential operators
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