Metric estimates for small denominators in multipoint problems for partial differential equations

Abstract: Conditions for well-posed solvability of multipoint problems for partial differential equations depend on lower estimates for the corresponding characteristic determinants. Using a metric approach and results on estimates for measures of exceptional sets of smooth functions we show that such estimates hold for almost all (with respect to Lebesgue measure) vectors whose coordinates are parameters of a problem such as coefficients of equations, values of interpolation nodes in multipoint conditions.

Ukrainiananalysis of PDEsfunctional analysisnumber theory

Audience: researchers in the discipline

Семінар з фрактального аналізу / Fractal analysis seminar

Series comments: Weekly research seminar on fractal analysis (online)

Topics:

• theory of fractals (fractal geometry and fractal analysis)
• Hausdorff–Besicovitch dimension, techniques and methods for its calculation and estimation
• functions and transformations preserving fractal (Hausdorff–Besicovitch, entropic, box-counting, packing, etc.) dimension
• sets of metric spaces that are essential for functions, sets, and dynamical systems
• self-similar, self-affine properties of mathematical objects
• systems of encoding for real numbers (numeral systems) and their applications
• metric number theory and metric theory of representations of numbers
• probabilistic number theory and probabilistic theory of representations of numbers
• measures supported on fractals, particularly singular measures and probability distributions
• nowhere monotonic and nowhere differentiable functions, functions with fractal properties
• theory of groups determined by invariants of transformations preserving tails of representation of numbers, digit frequencies, etc.

The talks are mostly in Ukrainian but English is also acceptable