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Department of         Mathematical Sciences
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Giovanni Leoni, Professor
Ph.D., University of Minnesota, Minneapolis
Office: Wean Hall 6123
Phone: 412-268-2557
Personal web site


Applied Analysis: Research in applied analysis is mostly centered around partial differential equations and calculus of variations, and is complemented by work in numerical analysis and scientific computation. This group pursues emerging areas of applied mathematics and mathematical analysis with special attention directed to issues which present interdisciplinary challenges in science and engineering. Recent areas of focus include: variational problems involving massive data and material defects; fluid-structure interactions over many scales, related to microscale .uid complexity, homogenization and mixing, and interfacial phenomena; and microstructural models of coarsening and random clustering. Faculty in this area have made fundamental contributions to the modeling, analysis and simulation of many of these notoriously difficult problems. This group has strong research and training collaborations with other CMU departments, such as the Biomedical Engineering, Computer Science, Materials Science and Engineering, Physics, and Statistics. Most faculty in applied analyis are permanent members of the Center for Nonlinear Analysis (CNA). For a detailed description of the CNA and its activities go to the CNA Home page.

Selected Publications:


Leoni, Giovanni, A first course in Sobolev spaces, Graduate Studies in Mathematics, 105. American Mathematical Society, Providence, RI, 2009.

Fonseca, Irene; Leoni, Giovanni, Modern methods in the calculus of variations: Lp spaces, Springer Monographs in Mathematics. Springer, New York, 2007.

Recent CNA Publications: