Communications on Pure and Applied Analysis (CPAA)

Beltrami equations in the plane and Sobolev regularity
Pages: 319 - 332, Issue 2, March 2018

doi:10.3934/cpaa.2018018      Abstract        References        Full text (413.3K)           Related Articles

Martí Prats - Departamento de Matemáticas, Universidad Autónoma de Madrid - ICMAT, Ciudad Universitaria de Cantoblanco - 28049 Madrid, Spain (email)

1 K. Astala, Area distortion of quasiconformal mappings, Acta Math., 173 (1994), 37-60.       
2 K. Astala, T. Iwaniec and G. Martin, Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane, vol. 48 of Princeton Mathematical Series, Princeton University Press, 2009.       
3 K. Astala, T. Iwaniec and E. Saksman, Beltrami operators in the plane, Duke Math. J., 107 (2001), 27-56.       
4 A. L. Baisón, A. Clop, R. Giova, J. Orobitg and A. P. di Napoli, Fractional differentiability for solutions of nonlinear elliptic equations, Potential Anal., 1-28.       
5 A. L. Baisón, La Ecuación de Beltrami Generalizada y Otras Ecuaciones Elípticas, PhD thesis, Universitat Autònoma de Barcelona, 2016.
6 A. L. Baisón, A. Clop and J. Orobitg, Beltrami equations with coefficient in the fractional Sobolev space $W^{\theta, \frac2\theta}$, Proc. Amer. Math. Soc., 145 (2017), 139-149.       
7 A. Clop, D. Faraco, J. Mateu, J. Orobitg and X. Zhong, Beltrami equations with coefficient in the Sobolev space $W^{1, p}$, Publ. Mat., 53 (2009), 197-230.       
8 A. Clop, D. Faraco and A. Ruiz, Stability of Calderón's inverse conductivity problem in the plane for discontinuous conductivities, Inverse Probl. Imaging, 4 (2010), 49-91.       
9 V. Cruz, J. Mateu and J. Orobitg, Beltrami equation with coefficient in Sobolev and Besov spaces, Canad. J. Math., 65 (2013), 1217-1235.       
10 M. Frazier, R. H. Torres and G. Weiss, The boundedness of Calderón-Zygmund Operators on the spaces $F^{\alpha, q}_p$., Rev. Mat. Iberoam., 4 (1988), 41-72.       
11 L. Grafakos, Classical Fourier Analysis, vol. 249 of Graduate Texts in Mathematics, 2nd edition, New York: Springer, 2008.       
12 S. Hofmann, An off-diagonal T1 Theorem and applications, J. Funct. Anal., 160 (1998), 581-622.       
13 T. Iwaniec, $L^p$-theory of quasiregular mappings, in Quasiconformal space mappings, Springer Berlin Heidelberg, 1992, 39-64.       
14 M. Prats, Sobolev regularity of quasiconformal mappings on domains, J. Anal. Math., to appear, arXiv: 1507.04332 [math.CA].
15 T. Runst and W. Sickel, Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations, vol. 3 of De Gruyter series in nonlinear analysis and applications, Walter de Gruyter; Berlin; New York, 1996.       
16 E. M. Stein, Singular Integrals and Differentiability Properties of Functions, vol. 30 of Princeton Mathematical Series, Princeton University Press, 1970.       
17 H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, vol. 18 of North-Holland Mathematical Library, North-Holland, 1978.       
18 H. Triebel, Theory of Function Spaces, Reprint (2010) edition, Birkhäuser, 1983.       
19 H. Triebel, Theory of Function Spaces III, vol. 100 of Monographs in Mathematics, Birkhäuser, 2006.       

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