p-Harmonic Tensors and Quasiregular Mappings

A linear boundary value problem for weakly quasiregular mappings in space

“…We recall that (see, e.g., Astala [2], Iwaniec [11], Iwaniec and Martin [14]) a map u from a domain Ω in R n to R n is said to be weakly Lquasiregular, L ≥ 1 being a constant called the (outer) dilatation of u, if it belongs to a (local) Sobolev space W 1,p loc (Ω; R n ) for some p ≥ 1 and satisfies…”

Lp-Mean coercivity, regularity and relaxation in the calculus of variations

“…Let n = m = k ≥ 2 and for L ≥ 1 let N (X ) = Ln n=2 det X: We can then recover from Theorems 7.1 and 7.3 some of results in [17,19,33,37] concerning the regularity of the so-called weakly L-quasiregular mappings.…”

“…The proof of Theorem 2.3 relies on a stability result of nonlinear Hodge decompositions due to Iwaniec [17] and Iwaniec and Sbordone [20]. We refer to [16,18,37] for other developments and to Lewis [21] for the related results using di erent methods involving the maximal functions in harmonic analysis.…”

“…This can be considered as a global version of the aforementioned results on the higher integrability of energy minimizers (see, e.g., [13][14][15]17,20,24]). …”

“…Some interesting applications of this result will be given in Section 7. The proof of Theorem 2.3 relies on an important technique of nonlinear Hodge decompositions of Iwaniec [17] and Iwaniec and Sbordone [20] (see also [16,21,37]). …”