Stratton Hall, 305A
Fernando Lopez Garcia
- Post-Doc Scholar, Mathematical Sciences
I am a visiting assistant professor in the Department of Mathematical Sciences and my research area is analysis. More specifically, I deal with the existence of solutions for the divergence equation in Sobolev spaces. This problem has been widely studied under different assumptions on the domains because of its applications. For example, it is fundamental for the variational analysis of the Stokes equations, which model the displacement of a viscous incompressible fluid. In particular, I am interested in studying the divergence problem on bad domains, i.e., domains with cusps and other irregularities, where it is necessary to consider weighted Sobolev spaces. Not only the divergence problem is of interest on bad domains, extension theorems and Korn inequality can also be mentioned.
Another of my passions is teaching. As a teacher one of the most enjoyable things is thinking about an exercise in class with the students and finding together different ways of approaching the problem and getting to a solution. The diversity in the students' backgrounds and majors at WPI makes this even more interesting and enriching. It is something I consider very valuable for everybody in the class.
- Divergence Operator
- Bad Domains
- Weighted Sobolev Spaces
- Korn Inequality
- Stokes Equations
- MS, Universidad de Buenos Aires, 2002
- PhD, Universidad de Buenos Aires, 2010
- G. Acosta, R. Durán, and F. López García, "Korn Inequality and Divergence Operator: Counterexamples and Optimality of Weighted Estimates," to appear in Proceedings of the American Mathematical Society, 2012
- R. Durán, and F. López García, "Solutions of the divergence and Korn inequalities on domains with an external cusp," Ann. Acad. Sci. Fennicae Mathematica, Vol. 35, 421-438, 2010
- R. Durán, and F. López García, "Solutions of the divergence and analysis of the Stokes equations in planar Holder-alpha domains," Math. Models and Methods in Appl. Sci., Vol. 20, 95-120, 2010