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In previous works, the homogenization of the problem with p-Laplace diffusion and nonlinear reaction in the boundary of periodically distributed particles in n-dimensional domains has been studied in the cases where $$p \le n$$ p≤n . The main trait of the cases $$p \le n$$ p≤n is the existence of a critical size of the particles, for which the nonlinearity arising of the limit problem does not coincide...
We get some necessary and sufficient conditions for the very weak solvability of the beam equation stated in terms of powers of the distance to the boundary, accordingly to the boundary condition under consideration. We get a L1-estimate by using an abstract result due to Crandall and Tartar. Applications to some nonlinear perturbed equations and to the eventual positivity of the solution of the...
We prove several uniform $$ L^1 $$ -estimates on solutions of a general class of one-dimensional parabolic systems, mainly coupled in the diffusion term, which, in fact, can be of degenerate type. They are uniform in the sense that they don’t depend on the coefficients, nor on the size of the spatial domain. The estimates concern the own solution or/and its spatial gradient. This paper extends...
An application of the results of this paper proves that there is not always an economic benefit when destroying the environment for planting an alternative industrial project. Our criterion, to act, to delay or to deny the industrial investment over the environment, is given in terms of the free boundary associated to a deterministic degenerate obstacle problem (on an unbounded domain) associated...
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