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Ball-Evans Approximation Problem

The Ball-Evans approximation problem asks whether a Sobolev homeomorphism between domains can be approximated strongly in the same Sobolev space by smooth diffeomorphisms onto the same target domain. For f:Omega->Lambda in W^(1,p), the desired convergence is

int_Omega(||f_j-f||^p+||Df_j-Df||^p)dx->0.

The approximating maps must be diffeomorphisms from Omega onto Lambda.

See also

Diffeomorphism, Homeomorphism, Sobolev Space

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References

Hencl, S. "Ball-Evans Approximation Problem: Recent Progress and Open Problems." J. Math. Sci. 298, 524-531, 2026. https://doi.org/10.1007/s10958-025-07739-8.

Cite this as:

Weisstein, Eric W. "Ball-Evans Approximation Problem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Ball-EvansApproximationProblem.html

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