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Published in last 50 years
We obtain a local weighted Caccioppoli-type estimate and prove the weighted version of the weak reverse Hölder inequality for A A -harmonic tensors.
AbstractWe prove a new energy or Caccioppoli type estimate for minimisers of the model functional ∫Ω|Du|2 + (det Du)2, where Ω ⊂ 2 and u: Ω → 2. We apply this to establish C∞ regularity for minimisers except on a closed set of measure zero. We also prove a maximum principle and use this to establish everywhere continuity of minimisers.
O. Introduction 1. Notation 2. Some exterior algebra 3. Differential forms in Lnm (i2, A n) 4. Differential systems for quasiregular mappings 5. Liouville Theorem in even dimensions 6. Hodge theory in LP(R n) 7. The Beltrami equation in even dimensions 8. The Beurling-Ahlfors operator 9. Regularity theorems for quasiregular mappings 10. The Caccioppoli type estimate 11. Removability theorems for quasiregular mappings 12. Some examples Appendix: The 4-dimensional case