The proposed research aims at (i) understanding the natural setting of frictions models from well-posedness
principles, (ii) developing a consistent integration theory, and (iii) investigating implications for optimization problems.
Among the topics are the Laplace equation, the well-posedness
of the water waves equations, shallow water asymptotics, deep water models and modulation equations, and water waves with surface tension.
Hu: Parametric well-posedness
for variational inequalities defined by bifunction, Comput.
After recalling an abstract well-posedness and preconditioning result , we use this theory to construct a parameter-robust preconditioner for our problem.
Well-posedness in some non-standard norms: a constructive approach.
So far, we obtained a well-posedness result for our problem with the nice parameterindependent constants 1/[square root of 5] and 2.
Among the topics are fractional calculus associated with doubling and non-doubling measures, some recent developments in the well-posedness
of non- linear dispersive equations, and variation inequalities for singular integrals and related operators.
when there are no Neumann-Neumann vertices), we also obtain a well-posedness result for the weight parameter [?
As in these papers, we use weighted Sobolev spaces, but our emphasis is not on singular functions, but rather on well-posedness results.
We exploit these results and spectral analysis to obtain a new well-posedness result in a properly augmented space [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.
eddy currents, potential formulation, well-posedness, finite elements, error estimates
5], where the well-posedness of some of these formulations is analyzed, and another one by Biro and Valli  with the analysis of one such formulation in a general topological setting.