The three-dimensional Ball–Evans approximation problem

Resolves the three-dimensional Ball–Evans approximation problem: every W^{1,p} homeomorphism between arbitrary bounded domains in ℝ³, for 1\le p\lt \infty, is a strong W^{1,p} limit of smooth diffeomorphisms onto the same target.

Manuscripts (2)

Strong diffeomorphic approximation in three dimensions for 1≤p≤2

September 24, 2026 · source · cite as \cite{OAI:Strong-diffeomorphic-approximation-in-three-dimensions-for-1-le-p-le-2-September-24-2026}

We resolve the three-dimensional Ball–Evans approximation problem for 1\le p\le2. Every W^{1,p} homeomorphism between arbitrary bounded domains in ℝ³ is a strong W^{1,p} limit of smooth diffeomorphisms onto the same target.

Strong diffeomorphic approximation in three dimensions for p>2

September 24, 2026 · source · cite as \cite{OAI:Strong-diffeomorphic-approximation-in-three-dimensions-for-p-gt-2-September-24-2026}

We resolve the three-dimensional Ball–Evans approximation problem for every finite p > 2. Every W^{1,p} homeomorphism between arbitrary bounded domains in ℝ³ can be approximated strongly in W^{1,p} by smooth diffeomorphisms onto the same target.

Result 368 · Partial differential equations. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.