We prove that a variant of the Hencl’s notion of AC^n λ-mapping (see [S. Hencl, On the notions of absolute continuity for functions of several variables, Fund. Math. 173 (2002) 175–189]), in which λ is not a constant, produces a new solution to the problem of regularity in the Sobolev space W^{1,N}_loc .
Bongiorno, D. (2009). On the problem of regularity in the Sobolev space W_loc^1,n. TOPOLOGY AND ITS APPLICATIONS, 156, 2986-2995 [10.1016/j.topol.2008.12.041].
On the problem of regularity in the Sobolev space W_loc^1,n.
BONGIORNO, Donatella
2009-01-01
Abstract
We prove that a variant of the Hencl’s notion of AC^n λ-mapping (see [S. Hencl, On the notions of absolute continuity for functions of several variables, Fund. Math. 173 (2002) 175–189]), in which λ is not a constant, produces a new solution to the problem of regularity in the Sobolev space W^{1,N}_loc .
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