Hide menu

Polopoly will be shut down December 15, 2023. Existing pages will have to be moved before or will be removed at that date. Empolyees may read more at FAQ Polopoly Avveckling

Singular Integral Operators on Lipschitz Surfaces

Numer of credits: 8 hp

Examiner: Vladimir Kozlov

Course literature: See below. Also various articles.

[1] B.E.J. Dahlberg, Harmonic Analysis and Partial Differential Equations, Technological Report, Chalmers University of Technology, 1985; references made to digital version available at http://www.math.chalmers.se/Math/Research/GeometryAnalysis/Lecturenotes/HAPE.ps [2009-01-07].

[2] G. Folland, Introduction to Partial Differential Equations, 2nd ed., Princeton University Press, Princeton, N.J. 1995.

[3] G.C. Hsiao and W.L. Wendland, Boundary Integral Equations, Applied Mathematical Sciences 164, Springer-Verlag, Berlin 2008.

[4] V. Maz'ya, Boundary Integral Equations; in V. Maz'ya and S.M. Nikol'skii, Encyclopaedia of Mathematical Sciences, Vol. 27, Springer-Verlag, Berlin 1991.

[5] Y. Meyer and R. Coifman, Wavelets: Calderón-Zygmund and multilinear operators, Cambridge University Press, Cambridge 1997.

[6] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, N.J. 1970.

[7] E. M. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton University Press, Princeton, N.J. 1993.

[8] E. M. Stein, Introduction to Fourier Analysis on Euclidian Spaces, Princeton University Press, 1975.

[9] M.E. Taylor, Tools for PDE: Pseudodifferential Operators, Paradifferential Operators, and Layer Potentials, Mathematical Surveys and Monographs 81, AMS, Providence, R.I. 2000.

Course contents: Singular integral operators. Riesz transforms. Operators of Calderón-Zygmund type. Pseudodifferential operators. Boundary Integral Methods and Layer Potentials. Riesz potentials. Lp-boundedness of the Cauchy integral operator on Lipschitz curves: different approaches. Layer Potentials on Lipschitz domains. BMO and the T1 theorem. Lp-results for Laplace equaion in Lipschitz domains.


Examination: Written and oral.

Prerequisites: MAI0001 Distributionsteori, MAI0063 Komplex analys, NM1002 Fourieranalys, MAI0067 Integrationsteori, MAI0065 Funktionalanalys (or equivalent courses).

Page manager: karin.johansson@liu.se
Last updated: 2023-04-03