TY - JOUR
T1 - Beltrami equations in the plane and Sobolev regularity
AU - Prats, Marti
N1 - Publisher Copyright:
© 2018 American Institute of Mathematical Sciences. All rights reserved.
PY - 2018/3
Y1 - 2018/3
N2 - New results regarding the Sobolev regularity of the principal solution of the linear Beltrami equation (formula presented) Bf for discontinuous Beltrami coefficients μ and v are obtained, using Kato-Ponce commutators, obtaining that Bf belongs to a Sobolev space with the same smoothness as the coefficients but some loss in the integrability parameter. A conjecture on the cases where the limitations of the method do not work is raised.
AB - New results regarding the Sobolev regularity of the principal solution of the linear Beltrami equation (formula presented) Bf for discontinuous Beltrami coefficients μ and v are obtained, using Kato-Ponce commutators, obtaining that Bf belongs to a Sobolev space with the same smoothness as the coefficients but some loss in the integrability parameter. A conjecture on the cases where the limitations of the method do not work is raised.
KW - Beltrami Equation
KW - Fractional Derivatives
KW - Kato-Ponce commutator
KW - Quasiconformal Mappings
KW - Sobolev Spaces
UR - http://www.scopus.com/inward/record.url?scp=85055637888&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1606.07751
DO - 10.48550/arXiv.1606.07751
M3 - Article
AN - SCOPUS:85055637888
SN - 1534-0392
VL - 17
SP - 319
EP - 332
JO - Communications on Pure and Applied Analysis
JF - Communications on Pure and Applied Analysis
IS - 2
ER -