Titlebook: Nonlinear Partial Differential Equations; The Abel Symposium 2 Helge Holden,Kenneth H. Karlsen Conference proceedings 2012 Springer-Verlag

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About Existence, Symmetry and Symmetry Breaking for Extremal Functions of Some Interpolation Functiberg (CKN) and weighted logarithmic Hardy (WLH) inequalities. These results have been obtained in a series of papers (Dolbeault et al. in Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 7(2):313–341, .; Dolbeault et al. in Adv. Nonlinear Stud. 9(4):713–726, .; Dolbeault, Esteban in Extremal functions for C

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,On the Oberbeck–Boussinesq Approximation on Unbounded Domains,in ... We provide a rigorous justification of the model by means of scale analysis of the full Navier–Stokes–Fourier system in the low Mach and Froude number regime on large domains, the diameter of which is proportional to the speed of sound. Finally, we show that the total energy of any solution o

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Surface Relaxation Below the Roughening Temperature: Some Recent Progress and Open Questions,ne one-dimensional step train (joint work with Hala Al Hajj Shehadeh and Jonathan Weare). The other addresses the finite-time flattening predicted by a fourth-order PDE model (joint work with Yoshikazu Giga). For each project we begin with a discussion of the mathematical model; then we summarize th

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On the Propagation of Oceanic Waves Driven by a Strong Macroscopic Flow,nal) stationary profile. This extends the study (Cheverry et al. in Semiclassical and spectral analysis of oceanic waves, Duke Math. J., accepted), where the profile was assumed to be zonal only and where explicit calculations were made possible due to the 1D setting..Here the diagonalization of the

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Nonlinear Diffusion with Fractional Laplacian Operators,sure is related to the density by an inverse fractional Laplacian operator. We prove existence of solutions that propagate with finite speed. The model has the very interesting property that mass preserving self-similar solutions can be found by solving an elliptic obstacle problem with fractional L