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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 ℝ

^{3}

, for

1\le p\lt \infty

, is a strong

W^{1,p}

limit of smooth diffeomorphisms onto the same target.

Manuscripts in this family · 2

Sep 24, 2026·main.pdf

We resolve the three-dimensional Ball–Evans approximation problem for

1\le p\le2

. Every

W^{1,p}

homeomorphism between arbitrary bounded domains in ℝ

^{3}

is a strong

W^{1,p}

limit of smooth diffeomorphisms onto the same target.

Full abstract

Sep 24, 2026·main.pdf

We resolve the three-dimensional Ball–Evans approximation problem for every finite p > 2. Every

W^{1,p}

homeomorphism between arbitrary bounded domains in ℝ

^{3}

can be approximated strongly in

W^{1,p}

by smooth diffeomorphisms onto the same target.

Full abstract