The directed distance between homotopy classes of critical Sobolev self-maps of spheres equals an explicit constant times the difference in their Brouwer degrees.
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Establishes optimal local well-posedness for reaction-diffusion SPDEs with non-trace-class multiplicative noise, critical initial-data spaces, instantaneous regularization, and applications to prototypical models.
Quantifies admissible Sobolev regularity for functions with zeros whose reciprocals are (p,q)-multipliers and refines Balian-Low uncertainty principles via connections to Gabor and shift-invariant systems.
citing papers explorer
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The distance between homotopy classes of Sobolev maps on spheres
The directed distance between homotopy classes of critical Sobolev self-maps of spheres equals an explicit constant times the difference in their Brouwer degrees.
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An optimal local theory for reaction-diffusion equations driven by non-trace-class noise
Establishes optimal local well-posedness for reaction-diffusion SPDEs with non-trace-class multiplicative noise, critical initial-data spaces, instantaneous regularization, and applications to prototypical models.