Analysis of PDEs

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Existence, uniqueness, and dynamics of partial differential equations.

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Mathematics

Proof Establishes Iwaniec’s Exact Beurling–Ahlfors Norm Conjecture

A quasiconvexity proof for a piecewise matrix integrand yields the exact $L^p$ operator norm: $p-1$ above $p=2$ and its reciprocal below.

math.APmath.CAmath.CV
Sep 25, 20264 min2609.28311
Mathematics

CDT Reduces Modes for Transport-Dominated Conservative PDEs

Mapping equal-mass 1D states into CDT space makes translations affine, yielding zero 2-width for linear transport and O(n⁻¹) shock-tolerant bounds.

math.APmath.NA
Jul 28, 20264 min2607.17066