Nonlinear Partial Differential Equations and their Applications
Auszeichung (distinction) for Ph.D. Thesis.
First prize of the Preisinstitut of the Universität Zürich for an outstanding dissertation.
Supported Fellow of the Schweizerische Studienstiftung from 1992-1996.
Research Fellowship of the Swiss National Science Foundation.
1999-2001: Von Karman Instructor, Applied Mathematics, California Institute of Technology.
1997-1999: Postdoctoral Scholar in the Swiss National Science Foundation Fellowship.
My research focuses on nonlinear Partial Differential Equations, in particular of elliptic and parabolic type and their applications. I am interested in well-posedness, regularity and global existence of solutions and their qualitative properties as well as some aspects of their numerical resolution.
(With J. Lambers) "Eigenvalue Characterization and Computation for the Laplacian on general 2D domains". To appear in Numerical Functional Analysis and Optimization.
(With J. Lambers) “Two New Nonlinear Nonlocal Diffusions for Noise Reduction”, to appear in Journal of Mathematical Imaging and Vision.
"Numerical Approximation of Generalized Functions: Aliasing, the Gibbs Phenomenon and a Numerical Uncertainty Principle", Functional Analysis and Evolution Equations, pp. 331-356, Birkhaeuser, Basel (2008).
“A globally well-posed nonlinear nonlocal diffusion”, Proceedings of ICIAM 2007, Zurich.
“Singular Elliptic and Parabolic Problems and a Class of Free Boundary Problems”, Proceedings of ICIAM 2007, Zurich.
"Optimal Regularity for a Class Singular Cauchy Problems", Journal of Differential Equations, Vol. 232, No. 2, pp 468-486 (2007).
"A Class of Free Boundary Problems with Onset of a new Phase", SIAM J. on Math. Anal., Vol. 36, No. 6, pp. 1981-2004 (2007).
(with J. Lambers and K. Solna) "1D Analysis of Wave Propagation in inhomogeneous media".
Numerical Functional Analysis and Optimization, Vol. 27 (1) 2006, 25-55.
"Generalized Fundamental Solutions ", Abstract and Applied Analysis no. 1 2005, 45-57.
"Elliptic and parabolic problems in unbounded domains". Mathematische Nachrichten, 272 (2004), pp. 32-44.
"A new first-kind boundary integral formulation for the the Laplace Dirichlet-to-Neumann map in 2D". Journal of Computational Physics 190 (2003), pp. 325-345.
"Problems in Unbounded Cylindrical Domains". Proceedings of the conference "Elliptic and Parabolic Problems: Recent Advances", NTHU, Taiwan (2003).
(With R. Pajarola and M. Sainz) "Object-Space Blending and Splatting". Sketches & Applications Catalog SIGGRAPH 2003. ACM, 2003.
"A 2D free boundary value problem and singular elliptic boundary value problems". Journal of Evolution Equations, Vol. 2 (4), 395--424 (2002).
(with D. Bernstein) "Modeling and analysis of hysteresis phenomena in electrostatic zipper actuators". Proceedings of Modeling and Simulation of Microsystems 2001, Hilton Head Island, SC, pp 306-309.
(with D. Bernstein and J. A. Pelesko) "Analytical and numerical analysis of electrostatically actuated MEMS devices". Proceedings of Modeling and Simulation of Microsystems 2000, San Diego, CA, pp 489-492.
(with S. Merino) "Gradual loss of positivity and hidden invariant cones in a scalar heat equation". Differential and integral equations, Vol.13 (10-12) (2000), pp 1551-1568.
"Diffusion in glassy polymers: sorption of a finite amount of swelling solvent". NoDEA 6 (1999), pp 297-317.
"Singular quasilinear abstract cauchy problems". Nonlinear Analysis TMA 32(5) (1998), pp 667-695.
(with J. Pelesko) "Transient instability in Case II diffusion". Journal of Polymer Science: Part B: Polymer Physics, Vol.36 (1998), pp 2941-2947.
"Diffusion in glassy polymers: a free boundary value problem". Advances in Mathematical Sciences and Applications, 7(2) (1997), pp 675-693.
(with S. Merino) "Hopf bifurcation in a scalar reaction diffusion equation". Journal of Differential Equations, 140 (1) (1997), pp 209-222.
NSF-CMS-0330470 (Co-Pi, 2003-2006) "Sensors: Broad-Bandwidth High-Resolution MEMS Array of Inertial Sensors with Embedded Optical Detection''
NSF-DMS-0712875 (single PI, 2007-2010) “Nonlinear Diffusions and Image Processing”