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Bilinear virial identities and applications

Fabrice Planchon, Luis Vega (2009)

Annales scientifiques de l'École Normale Supérieure

We prove bilinear virial identities for the nonlinear Schrödinger equation, which are extensions of the Morawetz interaction inequalities. We recover and extend known bilinear improvements to Strichartz inequalities and provide applications to various nonlinear problems, most notably on domains with boundaries.

Borel resummation of formal solutions to nonlinear Laplace equations in 2 variables

Maria Ewa Pliś, Bogdan Ziemian (1997)

Annales Polonici Mathematici

We consider a nonlinear Laplace equation Δu = f(x,u) in two variables. Following the methods of B. Braaksma [Br] and J. Ecalle used for some nonlinear ordinary differential equations we construct first a formal power series solution and then we prove the convergence of the series in the same class as the function f in x.

Boundary augmented Lagrangian method for the Signorini problem

Shougui Zhang, Xiaolin Li (2016)

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...

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