This collection of articles from the Proceedings of the Pan-American Advanced Studies Institute reflects recent developments in partial differential equations, nonlinear analysis and inverse problems. Interactions among these topics have produced remarkable developments over the last couple of decades. This volume contains survey articles reflecting the work of leading experts who presented minicourses at the event. Contributors include J. Busca, Y. Capdeboscq, M.S. Vogelius, F. A. Grunbaum, L. F. Matusevich, M. de Hoop, and P. Kuchment. The volume is suitable for graduate students and researchers interested in partial differential equations and their applications in nonlinear analysis and inverse problems.
Inverse scattering on the line with incomplete scattering data by T. Aktosun On universal inequalities for the low eigenvalues of the buckling problem by M. S. Ashbaugh Continuous and discrete inverse conductivity problems by J. Baras, C. Berenstein, and F. Gavilanez Connection between the Lieb-Thirring conjecture for Schrodinger operators and an isoperimetric problem for ovals on the plane by R. D. Benguria and M. Loss An introduction to PDE methods in finance by J. Busca A review of some recent work on impedance imaging for inhomogeneities of low volume fraction by Y. Capdeboscq and M. S. Vogelius Matrix bispectrality and Huygens' principle for Dirac operators by F. A. C. C. Chalub and J. P. Zubelli Well-posedness for the Schrodinger-Debye equation by A. J. Corcho and F. Linares On domains for which the clamped plate system is positivity preserving by A. Dall'Acqua and G. Sweers Entropy dissipation and Wasserstein metric methods for the viscous Burgers' equation: convergence to diffusive waves by M. Di Francesco and P. A. Markowich Remarks about the flashing rachet by J. Dolbeault, D. Kinderlehrer, and M. Kowalczyk A least action principle for steepest descent in a non-convex landscape by N. Ghoussoub and R. J. McCann A network tomography problem related to the hypercube by F. A. Grunbaum and L. F. Matusevich On the structure of the Schrodinger propagator by A. Hassell and J. Wunsch The downward continuation approach to modeling and inverse scattering of seismic data in the Kirchhoff approximation by M. V. de Hoop Approximate invariant manifold of the Allen-Cahn flow in two dimensions by M. Kowalczyk On some spectral problems of mathematical physics by P. Kuchment Inverse problem for a random potential by M. Lassas, L. Paivarinta, and E. Saksman Pseudodifferential analysis for the Laplacian on noncompact symmetric spaces by R. Mazzeo Boundary structure and cohomology of $b$-complex manifolds by G. A. Mendoza Unique continuation property for elliptic systems and crack determination in anisotropic elasticity by G. Nakamura, G. Uhlmann, and J.-N. Wang Duality in sub-supercritical bubbling in the Brezis-Nirenberg problem near the critical exponent by M. del Pino, J. Dolbeault, and M. Musso High-order domain variations in boundary value and free boundary problems by F. Reitich Radiation fields and inverse scattering on asymptotically Euclidean manifolds by A. S. Barreto Interactive oscillation sources in Signorini's type problems by C. Timofte and C. Conca Inverse scattering with time-periodic potentials by R. Weder A local Borg-Marchenko theorem for difference equations with complex coefficients by R. Weikard.