Titlebook: Extended Abstracts 2021/2022; Methusalem Lectures Duván Cardona,Joel Restrepo,Michael Ruzhansky Conference proceedings 2024 The Editor(s) (

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Nonlocal Functionals with Non-standard GrowthIn this note, we review recent progress on the De Giorgi–Nash–Moser theory for nonlocal functionals with non-standard growth, which include functionals with Orlicz growth, variable exponents, double phase growth, and orthotropic structure. Some open problems are suggested.

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Scattering of Maxwell Potentials on Curved SpacetimesWe report on the recent construction of a scattering theory for Maxwell potentials on curved spacetimes (Nicolas and Taujanskas, Conformal scattering of Maxwell potentials (2022). arXiv:2211.14579).

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Bounded Weak Solutions with Orlicz Space Data: An OverviewIt is well known that non-negative solutions to the Dirichlet problem . in a bounded domain ., where ., ., satisfy .. We generalize this result by replacing the Laplacian with a degenerate elliptic operator, and we show that we can take the data . in an Orlicz space . that, in the classical case, lies strictly between . and ., ..

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Recent Progress on the Mathematical Theory of Wave TurbulenceIn this note we review some recent progress on the mathematical theory of wave turbulence.

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On the Convergence Fourier Series and Greedy Algorithm by Multiplicative SystemIn this work we discuss the behavior of Fourier coefficients with respect to the multiplicative system (Vilenkin system), as well as convergence of the Fourier series and gredy algorithm with respect to the multiplicative system after modification of functions.

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Global Compactness, Subcritical Approximation of the Sobolev Quotient, and a Related Concentration RWe investigate some effects of the lack of compactness in the critical Sobolev embedding in the Heisenberg group.

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Duván Cardona,Joel Restrepo,Michael RuzhanskyHigh quality short research announcements, communications or summaries.Provide the most recent results and trends by some leading experts in analysis, PDEs and geometric analysis.Serve as a platform f

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