Abstract
We consider certain families of Dirichlet forms of diffusion type that describe the variational behaviour of possibly highly nonhomogeneous and nonisotropic bodies and we prove a structural Harnack inequality and Saint Venant type energy decays for their local solution. Estimates for the Green functions are also considered.
Sunto
Si considerano certe famiglie di forme di Dirichlet di tipo diffusione che descrivono il comportamento di corpi fortemente non omogenei e non isotropi e si provano per le relative soluzione locali una diseguaglianza di Harnack strutturale e stime tipo Saint Venant della decrescita dell'energia. Si studiano inoltre stime per la funzione di Green.
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Biroli, M., Mosco, U. A Saint-Venant type principle for Dirichlet forms on discontinuous media. Annali di Matematica pura ed applicata 169, 125–181 (1995). https://doi.org/10.1007/BF01759352
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DOI: https://doi.org/10.1007/BF01759352