This collection of contributed articles comprises the scientific program of the fifth annual Prairie Analysis Seminar. All articles represent important current advances in the areas of partial differential equations, harmonic analysis, and Fourier analysis. A range of interrelated topics is presented, with articles concerning Painleve removability, pseudodifferential operators, $A p$ weights, nonlinear Schrodinger equations, singular integrals, the wave equation, the Benjamin-Ono equation, quasi-geostrophic equations, quasiconformal mappings, integral inclusions, Bellman function methods, weighted gradient estimates, Hankel operators, and dynamic optimization problems. Most importantly, the articles illustrate the fruitful interaction between harmonic analysis, Fourier analysis, and partial differential equations, and illustrate the successful application of techniques and ideas from each of these areas to the others.
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978-0-8218-4093-1 (9780821840931)
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Schweitzer Klassifikation
Improved Painleve removability for bounded planar quasiregular mappings by K. Astala, A. Clop, J. Mateu, J. Orobitg, and I. Uriarte-Tuero Time-frequency estimates for pseudodifferential operators by A. Benyi and K. A. Okoudjou Extrapolation of operators defined on domains and boundary respecting $A_p$ weights by R. Berndt Existence, uniqueness and regularity of the free boundary in the Hele-Shaw problem with a degenerate phrase by I. A. Blank, M. K. Korten, and C. N. Moore On blowup solutions of NLS with low regularity initial data by J. Colliander Are $L^2$-bounded homogeneous singular integrals necessarily $L^p$-bounded? by L. Grafakos, P. Honzik, and D. Ryabogin A note on Chebyshev polynomials and finite difference wave equation by A. Grinshpan Complex-valued solutions of the Benjamin-Ono equation by A. D. Ionescu and C. E. Kenig The 2D quasi-geostrophic equations in the Sobolev space by N. Ju Convex functions and quasiconformal mappings by L. V. Kovalev and D. Maldonado Volterra integral inclusions: Existence of solutions by P. S. Macansantos Bellman function and the $H^1$-BMO duality by L. Slavin and A. Volberg Weights and Holder norms for solutions to a second order elliptic Dirichlet problem on nonsmooth domains by C. Sweezy Hankel operators and $VMO$ on the bi-disc by E. Terwilleger Necessary conditions for optimization problems governed by differential algebraic inclusions by L. Wang.
