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An augmented Lagrangian method, based on boundary variational formulations and fixed point method, is designed and analyzed for the Signorini problem of the Laplacian. Using the equivalence between Signorini boundary conditions and a fixed-point problem, we develop a new iterative algorithm that formulates the Signorini problem as a sequence of corresponding variational equations with the Steklov-Poincaré operator. Both theoretical results and numerical experiments show that the method presented...
We establish the existence of at least three weak solutions for the (p1,…,pₙ)-biharmonic system
⎧ in Ω,
⎨
⎩ on ∂Ω,
for 1 ≤ i ≤ n. The proof is based on a recent three critical points theorem.
We consider the homogenization of elliptic systems with -periodic coefficients. Classical two-scale approximation yields an error inside the domain. We discuss here the existence
of higher order corrections, in the case of general polygonal domains. The corrector depends in a non-trivial way on the boundary. Our analysis substantially extends previous results obtained for
polygonal domains with sides of rational slopes.
It is proved that a function can be estimated in the norm with a higher degree of summability if it satisfies some integral relations similar to the reverse Hölder inequalities (quasireverse Hölder inequalities). As an example, we apply this result to derive an a priori estimate of the Hölder norm for a solution of strongly nonlinear elliptic system.
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