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Project A7: Differential and integro-differential operators with degenerate coefficients


Principal Investigator(s)
Anna Balci
Lars Diening
Moritz Kaßmann
Visitor(s)
Currently no visitors.

Summary:

The project advances the regularity theory of elliptic and parabolic differential and integro-differential operators with degenerate coefficients. The main emphasis is on elliptic differential operators in divergence form with non-negative definite matrix-valued weights and integro-differential operators with non-negative kernels. We aim for higher integrability and Hölder continuity of solutions resp. their derivatives in settings, where classical ellipticity assumptions fail. We complement this by investigations of possible Lavrentiev phenomenons. Building upon our regularity results, we develop and analyze numerical methods including optimal adaptive approximation schemes.


Recent Preprints:

25023 Kyeong Bae Kim, Ho-Sik Lee, Simon Nowak PDF

Gradient estimates for nonlinear kinetic Fokker-Planck equations

Project: A7

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Gradient estimates for nonlinear kinetic Fokker-Planck equations


Authors: Kyeong Bae Kim, Ho-Sik Lee, Simon Nowak Projects: A7
Submission Date: 13.03.2025 Submitter: Moritz Kaßmann
Download: PDF Link: 25023

25022 Cristiana De Filippis, Giuseppe Mingione, Simon Nowak PDF

Partial regularity in nonlocal systems I

Project: A7

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Partial regularity in nonlocal systems I


Authors: Cristiana De Filippis, Giuseppe Mingione, Simon Nowak Projects: A7
Submission Date: 13.03.2025 Submitter: Moritz Kaßmann
Download: PDF Link: 25022

25018 Anna Balci, Linus Behn, Lars Diening, Johannes Storn PDF

Examples of p-harmonic maps

Project: A7, B7

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Examples of p-harmonic maps


Authors: Anna Balci, Linus Behn, Lars Diening, Johannes Storn Projects: A7, B7
Submission Date: 07.03.2025 Submitter: Martina Hofmanová
Download: PDF Link: 25018

24119 Linus Behn, Lars Diening, Jihoon Ok, Julian Rolfes PDF

Nonlocal equations with degenerate weights

Project: A7

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Nonlocal equations with degenerate weights


Authors: Linus Behn, Lars Diening, Jihoon Ok, Julian Rolfes Projects: A7
Submission Date: 07.03.2025 Submitter: Martina Hofmanová
Download: PDF Link: 24119

24112 Lars Diening, Kyeong Bae Kim, Ho-Sik Lee, Simon Nowak PDF

Gradient estimates for parabolic nonlinear nonlocal equations

Project: A7

Published: Calculus of Variations and Partial Differential Equations 64, no. 98 (2025)

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Gradient estimates for parabolic nonlinear nonlocal equations


Authors: Lars Diening, Kyeong Bae Kim, Ho-Sik Lee, Simon Nowak Projects: A7
Submission Date: 13.03.2025 Submitter: Moritz Kaßmann
Download: PDF Link: 24112
Published: Calculus of Variations and Partial Differential Equations 64, no. 98 (2025)

24111 Lars Diening, Kyeong Bae Kim, Ho-Sik Lee, Simon Nowak PDF

Higher differentiability for the fractional p-Laplacian

Project: A7

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Higher differentiability for the fractional p-Laplacian


Authors: Lars Diening, Kyeong Bae Kim, Ho-Sik Lee, Simon Nowak Projects: A7
Submission Date: 13.03.2025 Submitter: Moritz Kaßmann
Download: PDF Link: 24111

24110 Linus Behn, Lars Diening, Simon Nowak, Toni Scharle PDF

The De Giorgi method for local and nonlocal systems

Project: A7

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The De Giorgi method for local and nonlocal systems


Authors: Linus Behn, Lars Diening, Simon Nowak, Toni Scharle Projects: A7
Submission Date: 13.03.2025 Submitter: Moritz Kaßmann
Download: PDF Link: 24110

24109 Lars Diening, Kyeong Bae Kim, Ho-Sik Lee, Simon Nowak PDF

Nonlinear nonlocal potential theory at the gradient level

Project: A7

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Nonlinear nonlocal potential theory at the gradient level


Authors: Lars Diening, Kyeong Bae Kim, Ho-Sik Lee, Simon Nowak Projects: A7
Submission Date: 13.03.2025 Submitter: Moritz Kaßmann
Download: PDF Link: 24109

24023 Anna Balci, Ho-Sik Lee PDF

Zaremba problem with degenerate weights

Project: A7

Published: Advances in Calculus of Variations (2024)

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Zaremba problem with degenerate weights


Authors: Anna Balci, Ho-Sik Lee Projects: A7
Submission Date: 15.04.2024 Submitter: L’ubomír Baňas
Download: PDF Link: 24023
Published: Advances in Calculus of Variations (2024)

23120 Anna Balci, Lars Diening, Mikhail Surnachev PDF

Scalar minimizers with maximal singular sets and lack of Meyers property

Project: A7

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Scalar minimizers with maximal singular sets and lack of Meyers property


Authors: Anna Balci, Lars Diening, Mikhail Surnachev Projects: A7
Submission Date: 11.01.2024 Submitter: Martina Hofmanová
Download: PDF Link: 23120


All Publications of this Project


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