Dirk Pauly @ TUDD

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Publications

Submitted and Accepted

  1. P.D. Lamberti, D. Pauly, and M. Zaccaron, Shape Derivatives of the Eigenvalues of the De Rham Complex for Lipschitz Deformations and Variable Coefficients: Part I, 2024
    arXiv PDF
  2. D. Pauly and N. Skrepek, Weak Equals Strong L2-Regularity for Partial Tangential Traces on Lipschitz Domains, 2023
    arXiv PDF

Books

  1. U. Langer, D. Pauly, and S. Repin (Eds.), Maxwell's Equations: Analysis and Numerics, Radon Series on Computational and Applied Mathematics (24), De Gruyter, Berlin, 2019 (434p, ISBN 978-3-11-054264-6)
    De Gruyter PDF

Journal Articles and Book Chapters

  1. D. Pauly and R. Picard, Families of Annihilating Skew-Selfadjoint Operators and their Connection to Hilbert Complexes, Advances in Computational Mathematics, 2024
    arXiv PDF
  2. D. Pauly and M. Schomburg, Hilbert Complexes with Mixed Boundary Conditions - Part 3: Biharmonic Complexes, Mathematical Methods in the Applied Sciences, 47(6), 3847-3892, 2024
    arXiv PDF
  3. R. Hiptmair, D. Pauly, and E. Schulz, Traces for Hilbert Complexes, Journal of Functional Analysis, 284(10), 50pp, 2023
    arXiv PDF
  4. D. Pauly and N. Skrepek, A Compactness Result for the div-curl System with Inhomogeneous Mixed Boundary Conditions for Bounded Lipschitz Domains and Some Applications, Annali dell' Universita di Ferrara, 69(2), 505-519, 2023
    arXiv PDF
  5. D. Pauly and W. Zulehner, The Elasticity Complex: Compact Embeddings and Regular Decompositions, Applicable Analysis, 102(16), 4393-4421, 2023
    arXiv PDF
  6. D. Pauly and M. Waurick, The Index of some Mixed Order Dirac-Type Operators and Generalised Dirichlet-Neumann Tensor Fields, Mathematische Zeitschrift, 301(2), 1739-1819, 2022
    arXiv PDF
  7. D. Pauly and M. Schomburg, Hilbert Complexes with Mixed Boundary Conditions - Part 2: Elasticity Complex, Mathematical Methods in the Applied Sciences, 45(16), 8971-9005, 2022
    arXiv PDF
  8. D. Pauly and M. Schomburg, Hilbert Complexes with Mixed Boundary Conditions - Part 1: De Rham Complex, Mathematical Methods in the Applied Sciences, 45(5), 2465-2507, 2022
    arXiv PDF
  9. S. Kurz, D. Pauly, D. Praetorius, S.I. Repin, and D. Sebastian, Functional A Posteriori Error Estimates for Boundary Element Methods, Numerische Mathematik, 147(4), 937-966, 2021
    arXiv PDF
  10. D. Pauly, R. Picard, S. Trostorff, and M. Waurick, On a Class of Degenerate Abstract Parabolic Problems and Applications to Some Eddy Current Models, Journal of Functional Analysis, 280(7), 45pp, 2021
    arXiv PDF
  11. D. Pauly and W. Zulehner, The divDiv-Complex and Applications to Biharmonic Equations, Applicable Analysis, 99(9), 1579-1630, 2020
    arXiv PDF
  12. F. Osterbrink and D. Pauly, Low Frequency Asymptotics and Electro-Magneto-Statics for Time-Harmonic Maxwell's Equations in Exterior Weak Lipschitz Domains with Mixed Boundary Conditions, SIAM Journal on Mathematical Analysis, 52(5), 4971-5000, 2020
    arXiv PDF
  13. D. Pauly and J. Valdman, Poincaré-Friedrichs Type Constants for Operators Involving grad, curl, and div: Theory and Numerical Experiments, Computers and Mathematics with Applications, 79, 3027-3067, 2020
    arXiv PDF
  14. D. Pauly, Solution Theory, Variational Formulations, and Functional a Posteriori Error Estimates for General First Order Systems with Applications to Electro-Magneto-Statics and More, Numerical Functional Analysis and Optimization, 41(1), 16-112, 2020
    arXiv PDF
  15. D. Pauly, On the Maxwell and Friedrichs/Poincare Constants in ND, Mathematische Zeitschrift, 293(3), 957–987, 2019
    arXiv PDF
  16. D. Pauly, A Global div-curl-Lemma for Mixed Boundary Conditions in Weak Lipschitz Domains and a Corresponding Generalized A0*-A1-Lemma in Hilbert Spaces, Analysis (Munich), 39(2), 33-58, 2019
    arXiv PDF
  17. F. Osterbrink and D. Pauly, Time-Harmonic Electro-Magnetic Scattering in Exterior Weak Lipschitz Domains with Mixed Boundary Conditions, Maxwell’s Equations: Analysis and Numerics (Radon Series on Computational and Applied Mathematics 24), 341-382, De Gruyter, Berlin, 2019
    arXiv PDF
  18. S. Bauer, D. Pauly, and M. Schomburg, Weck's Selection Theorem: The Maxwell Compactness Property for Bounded Weak Lipschitz Domains with Mixed Boundary Conditions in Arbitrary Dimensions, Maxwell’s Equations: Analysis and Numerics (Radon Series on Computational and Applied Mathematics 24), 77-104, De Gruyter, Berlin, 2019
    arXiv PDF
  19. D. Pauly and S.I. Repin, A Posteriori Estimates for the Stationary Stokes Problem in Exterior Domains, Algebra i Analiz, 31(3), 184-215, 2019; St. Petersburg Mathematical Journal, 31(3), 533-555, 2020;
    arXiv PDF PDF (SPMJ)
  20. I. Anjam and D. Pauly, An Elementary Method of Deriving A Posteriori Error Equalities and Estimates for Linear Partial Differential Equations, Computational Methods in Applied Mathematics, 19(2), 311-322, 2019
    arXiv PDF
  21. D. Pauly and R. Picard, A Note on the Justification of the Eddy Current Model in Electrodynamics, Mathematical Methods in the Applied Sciences, 40(18), 7104-7109, 2017
    arXiv PDF
  22. D. Pauly and I. Yousept, A Posteriori Error Analysis for the Optimal Control of Magneto-Static Fields, ESAIM: Mathematical Modelling and Numerical Analysis, 51(6), 2159-2191, 2017
    arXiv PDF
  23. D. Pauly, On the Maxwell Constants in 3D, Mathematical Methods in the Applied Sciences, 40(2), 435-447, 2017
    arXiv PDF
  24. S. Bauer and D. Pauly, On Korn's First Inequality for Mixed Tangential and Normal Boundary Conditions on Bounded Lipschitz-Domains in RN, Annali dell'Universita di Ferrara, 62(2), 173-188, 2016
    arXiv PDF
  25. S. Bauer and D. Pauly, On Korn's First Inequality for Tangential or Normal Boundary Conditions with Explicit Constants, Mathematical Methods in the Applied Sciences, 39(18), 5695-5704, 2016
    arXiv PDF
  26. I. Anjam and D. Pauly, Functional a posteriori error control for conforming mixed approximations of coercive problems with lower order terms, Computational Methods in Applied Mathematics, 16(4), 609-631, 2016
    arXiv PDF
  27. S. Bauer, D. Pauly, and M. Schomburg, The Maxwell Compactness Property in Bounded Weak Lipschitz Domains with Mixed Boundary Conditions, SIAM Journal on Mathematical Analysis, 48(4), 2912-2943, 2016
    arXiv PDF
  28. S. Bauer, P. Neff, D. Pauly, and G. Starke, Dev-Div and DevSym-DevCurl Inequalities for Incompatible Square Tensor Fields with Mixed Boundary Conditions, ESAIM: Control, Optimisation and Calculus of Variations, 22, 112-133, 2016
    arXiv PDF
  29. P. Neff, D. Pauly, and K. J. Witsch, Poincaré meets Korn via Maxwell: Extending Korn's First Inequality to Incompatible Tensor Fields, Journal of Differential Equations, 258, 1267-1302, 2015
    arXiv PDF
  30. D. Pauly, On Maxwell's and Poincaré's Constants, Discrete and Continuous Dynamical Systems - Series S, 8(3), 607-618, 2015
    arXiv PDF
  31. D. Pauly, On Constants in Maxwell Inequalities for Bounded and Convex Domains, Zapiski POMI, 435, 46-54, 2014; Journal of Mathematical Sciences (Springer New York), 210(6), 787-792, 2015
    arXiv PDF (Zapiski POMI) PDF (J. Math. Sci.)
  32. S. Bauer, P. Neff, D. Pauly, and G. Starke, New Poincaré-Type Inequalities, Comptes Rendus Mathématique, Académie des Sciences Paris, Ser. I, 352, 163-166, 2014
    arXiv PDF
  33. P. Neff, D. Pauly, and K.-J. Witsch, On an Extension of Korn's First Inequality to Incompatible Tensor Fields on Domains of Arbitrary Dimensions, Modeling, Simulation and Optimization for Science and Technology, Computational Methods in Applied Sciences 34, 139-159, Springer, 2014
    arXiv PDF
  34. J. Lankeit, P. Neff, and D. Pauly, Unique Continuation for First Order Systems with Integrable Tensor Coefficients and Applications to Elasticity and Plasticity, Comptes Rendus Mathématique, Académie des Sciences Paris, Ser. I, 351, 247-250, 2013
    arXiv PDF
  35. J. Lankeit, P. Neff, and D. Pauly, Uniqueness of integrable solutions to first order systems with integrable tensor-coefficients and applications to elasticity, Zeitschrift für Angewandte Mathematik und Physik, 64, 1679-1688, 2013
    arXiv PDF
  36. O. Mali, A. Muzalevskiy, and D. Pauly, Conforming and Non-Conforming Functional A Posteriori Error Estimates for Elliptic Boundary Value Problems in Exterior Domains: Theory and Numerical Tests, Russian Journal of Numerical Analysis and Mathematical Modelling, 28(6), 577-596, 2013
    arXiv PDF
  37. P. Neff, D. Pauly, and K. J. Witsch, Maxwell meets Korn: A New Coercive Inequality for Tensor Fields in RNxN with Square-Integrable Exterior Derivative, Mathematical Methods in the Applied Sciences, 35(1), 65-71, 2012
    arXiv PDF
  38. D. Pauly, On Polynomial and Exponential Decay of Eigen-Solutions to Exterior Boundary Value Problems for the Generalized Time-Harmonic Maxwell System, Asymptotic Analysis, 79(1-2), 133-160, 2012
    arXiv PDF
  39. P. Neff, D. Pauly, and K. J. Witsch, A Canonical Extension of Korn's First Inequality to H(Curl) motivated by Gradient Plasticity with Plastic Spin, Comptes Rendus Mathématique, Académie des Sciences Paris, Ser. I, 349, 1251-1254, 2011
    arXiv PDF
  40. P. Neff, D. Pauly, and K. J. Witsch, On a Canonical Extension of Korn's First and Poincaré's Inequality to H(Curl), Zapiski POMI, 397, 115-125, 2011; Journal of Mathematical Sciences (Springer New York), 185(1), 64-70, 2012
    arXiv PDF (Zapiski POMI) PDF (J. Math. Sci.)
  41. D. Pauly, S. Repin, and T. Rossi, Estimates for Deviations from Exact Solutions of the Cauchy Problem for Maxwell's Equations, Annales Academiae Scientiarium Fennicae Mathematica, 36, 661-676, 2011
    arXiv PDF
  42. D. Pauly and T. Rossi, Theoretical Considerations on the Computation of Generalized Time-Periodic Waves, Advances in Mathematical Sciences and Applications, 21 (1), 105-131, 2011
    arXiv PDF
  43. P. Kuhn and D. Pauly, Regularity Results for Generalized Electro-Magnetic Problems, Analysis (Munich), 30, 225-252, 2010
    arXiv PDF
  44. D. Pauly and S. Repin, Functional A Posteriori Error Estimates for Elliptic Problems in Exterior Domains, Problemy Matematicheskogo Analiza, 42, 83-94, 2009; Journal of Mathematical Sciences (Springer New York), 162(3), 393-406, 2009
    arXiv PDF (Problemy Matematicheskogo Analiza) PDF (J. Math. Sci.)
  45. D. Pauly and S. Repin, Two-Sided A Posteriori Error Bounds for Electro-Magneto Static Problems, Zapiski POMI, 370, 94-110, 2009; Journal of Mathematical Sciences (Springer New York), 166(1), 53-62, 2010
    arXiv PDF (Zapiski POMI) PDF (J. Math. Sci.)
  46. D. Pauly, Complete Low Frequency Asymptotics for Time-Harmonic Generalized Maxwell Equations in Nonsmooth Exterior Domains, Asymptotic Analysis, 60(3-4), 125-184, 2008
    arXiv PDF
  47. D. Pauly, Hodge-Helmholtz Decompositions of Weighted Sobolev Spaces in Irreular Exterior Domains with Inhomogeneous and Anisotropic Media, Mathematical Methods in the Applied Sciences, 31(13), 1509-1543, 2008
    arXiv PDF
  48. D. Pauly, Generalized Electro-Magneto Statics in Nonsmooth Exterior Domains, Analysis (Munich), 27, 425-464, 2007
    arXiv PDF
  49. D. Pauly, Low Frequency Asymptotics for Time-Harmonic Generalized Maxwell Equations in Nonsmooth Exterior Domains, Advances in Mathematical Sciences and Applications, 16 (2), 591-622, 2006
    arXiv PDF

Proceedings

  1. A.M. Alonso Rodriguez, D.N. Arnold, D. Pauly, F. Rapetti (Eds.), Full-workshop: Hilbert Complexes: Analysis, Applications, and Discretizations. Abstracts from the full-workshop held June 19–25, 2022, Oberwolfach Rep. 29, 57p, 2022
  2. M. Dauge, U. Langer, P. Monk, D. Pauly (Eds.), Mini-workshop: Mathematical and numerical analysis of Maxwell’s equations. Abstracts from the mini-workshop held December 16–22, 2018, Oberwolfach Rep. 15(4), 3349-3374, 2018
  3. D. Pauly, A Global div-curl-Lemma for Mixed Boundary Conditions in Weak Lipschitz Domains, Proceedings of Wave Phenomena, KIT, 2018 - arXiv, PDF
  4. S. Bauer, P. Neff, D. Pauly, and G. Starke, Some Poincaré type inequalities for quadratic matrix fields, Proceedings in Applied Mathematics and Mechanics (PAMM), 13, 359-360, 2013 - PDF
  5. J. Lankheit, P. Neff, and D. Pauly, Unique Continuation for First Order Systems with Integrable Tensor Coefficients and Applications to Elasticity and Plasticity, Proceedings in Applied Mathematics and Mechanics (PAMM), 13, 361-362, 2013 - PDF
  6. P. Neff, D. Pauly, and K. J. Witsch, A Korn's inequality for incompatible tensor fields, Proceedings in Applied Mathematics and Mechanics (PAMM), 11, 683-684, 2011 - PDF

Unpublished Stuff

  1. P.D. Lamberti, D. Pauly, and M. Zaccaron, Shape Derivatives of Eigenvalues of the De Rham Complex, 2024
    arXiv
  2. I. Anjam and D. Pauly, A Short Note on a Weighted Friedrichs Inequality, 2018
    arXiv
Dirk Pauly

dirk.pauly@tu-dresden.de
Institut für Analysis
TU Dresden

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