Titlebook: Harmonic Analysis, Partial Differential Equations and Applications; In Honor of Richard Sagun Chanillo,Bruno Franchi,Eric T. Sawyer Book 2

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Smoluchowski Equation with Variable Coefficients in Perforated Domains: Homogenization and Applicatnts depend on all variables, in particular on the microscopic variable. This system modelizes the aggregation and diffusion of the .-amyloid peptide A.. in the cerebral tissue, a process associated with the development of Alzheimer’s disease. Our homogenization result, based on Allaire-Nguetseng two

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Chern-Moser-Weyl Tensor and Embeddings into Hyperquadrics, how to find an accessible way to tell whether two objects are in the same equivalence class. A general approach to this problem is to find a complete set of (geometric, analytic or algebraic) invariants. In the subject of Several Complex Variables and Complex Geometry, a fundamental problem is to c

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A Good-, Lemma, Two Weight ,1 Theorems Without Weak Boundedness, and a Two Weight Accretive Global e as side conditions the . conditions, punctured ... conditions, and certain .. Then the weak boundedness property associated with the operator .. and the weight pair ., is ‘good-.’ controlled by the testing conditions and the Muckenhoupt and energy?conditions. As a consequence, assuming the side co

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Intrinsic Difference Quotients,tients is provided. It is also shown how intrinsic difference quotients along horizontal directions are naturally related with the intrinsic derivatives, introduced e.g. in Franchi et?al. (Comm Anal Geom 11(5):909–944, 2003) and Ambrosio et?al. (J Geom Anal 16:187–232, 2006) and used to characterize

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Weighted Norm Inequalities of (1, ,)-Type for Integral and Fractional Maximal Operators,ith nonnegative kernel, . These problems are motivated by sublinear elliptic equations in a domain . with non-trivial Green’s function .(.,?.) associated with the Laplacian, fractional Laplacian, or more general elliptic operator. We also treat fractional maximal operators .. (0?≤?.?

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,New Bellman Functions and Subordination by Orthogonal Martingales in ,,, 1 < , ≤ 2,metries. Our Bellman function is obtained by explicitly solving a corresponding Monge–Ampère equation. In one particular case this Bellman function can be given by an explicit and simple formula. This corresponds to . = 3∕2.