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### Boundary augmented Lagrangian method for the Signorini problem

Applications of Mathematics

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...

### Existence of positive bounded solutions for some nonlinear polyharmonic elliptic systems.

Electronic Journal of Differential Equations (EJDE) [electronic only]

### Existence of three solutions for a class of (p₁,...,pₙ)-biharmonic systems with Navier boundary conditions

Annales Polonici Mathematici

We establish the existence of at least three weak solutions for the (p1,…,pₙ)-biharmonic system ⎧$\Delta \left(|\Delta {u}_{i}{|}^{p-2}\Delta {u}_{i}\right)=\lambda {F}_{{u}_{i}}\left(x,u₁,\dots ,uₙ\right)$ in Ω, ⎨ ⎩${u}_{i}=\Delta {u}_{i}=0$ on ∂Ω, for 1 ≤ i ≤ n. The proof is based on a recent three critical points theorem.

### Homogenization in polygonal domains

Journal of the European Mathematical Society

We consider the homogenization of elliptic systems with $\epsilon$-periodic coefficients. Classical two-scale approximation yields an $O\left(\epsilon \right)$ 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.

### Quasireverse Hölder inequalities and a priori estimates for strongly nonlinear systems

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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.

### Sur la régularité des solutions faibles des équations elliptiques non linéaires

Commentationes Mathematicae Universitatis Carolinae

### К теории общих линейных краевых задач для эллиптических систем

Sibirskij matematiceskij zurnal

### Разрешимость краевых задач для общих эллиптических систем

Matematiceskij sbornik

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