Publications
Submitted and in preparation
- S. Probst and C. Schneider, “Improved universal approximation with neural networks
studied via affine-invariant subspaces of L_2(IR^n)”, submitted, 2024. - M. Hansen and C. Schneider, “Refined localizaton spaces, Kondratiev spaces with fractional smoothness and extension operators“, submitted, 2024.
- C. Schneider, M. Ullrich, and J. Vybiral, “Approximation and sampling for deep ReLU neural networks“, in preparation.
- S. Dahlke and C. Schneider, “Besov regularity of non-linear parabolic PDEs on non-convex
polyhedral domains“, in preparation.
Publications
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Embeddings and pointwise multiplication in Kondratiev spaces on polyhedral type domains
In: Zeitschrift für Analysis und ihre Anwendungen (2024)
ISSN: 0232-2064
URL: https://arxiv.org/abs/1911.01962
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Direct estimates for adaptive time-stepping finite element methods
In: Journal of Complexity (2024)
ISSN: 0885-064X
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Multivariate Riesz basis of ReLU neural networks
In: Applied and Computational Harmonic Analysis 68 (2024), Article No.: 101605
ISSN: 1063-5203
DOI: 10.1016/j.acha.2023.101605
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Path Regularity of the Brownian Motion and the Brownian Sheet
In: Constructive Approximation 59 (2023), p. 485-539
ISSN: 0176-4276
DOI: 10.1007/s00365-023-09647-z
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Besov regularity of inhomogeneous parabolic PDEs
In: Partial Differential Equations and Applications 4 (2023), Article No.: 43
ISSN: 2662-2963
DOI: 10.1007/s42985-023-00262-y
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On approximation classes for adaptive time-stepping finite element methods
In: IMA Journal of Numerical Analysis (2022)
ISSN: 0272-4979
DOI: 10.1093/imanum/drac056
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Anisotropic Besov Regularity of parabolic PDEs
In: Pure and Applied Functional Analysis (2022)
ISSN: 2189-3764
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Sobolev meets Besov: Regularity for the Poisson equation with Dirichlet, Neumann and mixed boundary values
In: Analysis and Applications (2022)
ISSN: 0219-5305
DOI: 10.1142/s0219530522500026
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An extension operator for Sobolev spaces with mixed weights
In: Mathematische Nachrichten (2022)
ISSN: 0025-584X
DOI: 10.1002/mana.202000590
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Growth Envelopes of some variable and mixed function spaces.
In: Journal of Geometric Analysis (2021)
ISSN: 1050-6926
DOI: 10.1007/s12220-021-00811-0
URL: http://arxiv.org/abs/2007.08210
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Beyond Sobolev and Besov: Regularity of Solutions of PDEs and Their Traces in Function Spaces
Cham: Springer, 2021
(Lecture Notes in Mathematics, Vol.2291)
ISBN: 978-3-030-75138-8
DOI: 10.1007/978-3-030-75139-5
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Regularity in Sobolev and Besov spaces for parabolic problems on domains of polyhedral type
In: Journal of Geometric Analysis (2021)
ISSN: 1050-6926
DOI: 10.1007/s12220-021-00700-6
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No publications found.
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Traces of shearlet coorbit spaces on domains
In: Applied Mathematics Letters 91 (2019), p. 35-40
ISSN: 0893-9659
DOI: 10.1016/j.aml.2018.11.019
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Besov regularity of parabolic and hyperbolic PDEs
In: Analysis and Applications 17 (2019), p. 235-291
ISSN: 0219-5305
DOI: 10.1142/S0219530518500306
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Symmetries on manifolds: generalizations of the radial lemma of Strauss
In: Revista Matematica Complutense 32 (2019), p. 365-393
ISSN: 1139-1138
DOI: 10.1007/s13163-018-0285-2
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Traces and extensions of generalized smoothness Morrey spaces on domains
In: Nonlinear Analysis - Theory Methods & Applications 181 (2019), p. 311-339
ISSN: 0362-546X
DOI: 10.1016/j.na.2019.01.003
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On Besov regularity of solutions to nonlinear elliptic partial differential equations
In: Nonlinear Analysis - Theory Methods & Applications (2019)
ISSN: 0362-546X
DOI: 10.1007/s13163-012-0093-z
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Describing the singular behaviour of parabolic equations on cones in fractional Sobolev spaces
In: GEM - International Journal on Geomathematics 9 (2018), p. 293-315
ISSN: 1869-2672
DOI: 10.1007/s13137-018-0106-2
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Morrey spaces on domains:Different approaches and growth envelopes
In: Journal of Geometric Analysis 28 (2018), p. 817-841
ISSN: 1050-6926
DOI: 10.1007/s12220-017-9843-y
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Unboundedness properties of smoothness Morrey spaces of regular distributions
In: Science China-Mathematics 60 (2017), p. 2349-2376
ISSN: 1674-7283
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No publications found.
No publications found.
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Spaces of generalized smoothness in the critical case: optimal embeddings, continuity envelopes and approximation numbers
In: Journal of Approximation Theory 187 (2014), p. 82--117
ISSN: 0021-9045
DOI: 10.1016/j.jat.2014.07.010
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Sobolev spaces on Riemannian manifolds with bounded geometry: general coordinates and traces
In: Mathematische Nachrichten 286 (2013), p. 1586--1613
ISSN: 0025-584X
DOI: 10.1002/mana.201300007
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On trace spaces of 2-microlocal Besov spaces with variable integrability
In: Mathematische Nachrichten 286 (2013), p. 1240--1254
ISSN: 0025-584X
DOI: 10.1002/mana.201200092
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Non-smooth atomic decompositions, traces on Lipschitz domains, and pointwise multipliers in function spaces
In: Journal of Functional Analysis 264 (2013), p. 1197--1237
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2012.12.005
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Homogeneity property of Besov and Triebel-Lizorkin spaces
In: Journal of Function Spaces and Applications (2012), p. Art. ID 281085, 17
ISSN: 0972-6802
DOI: 10.1155/2012/281085
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Trace operators on fractals, entropy and approximation numbers
In: Georgian Mathematical Journal 18 (2011), p. 549--575
ISSN: 1072-947X
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Traces of Besov and Triebel-Lizorkin spaces on domains
In: Mathematische Nachrichten 284 (2011), p. 572--586
ISSN: 0025-584X
DOI: 10.1002/mana.201010052
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Optimal embeddings of spaces of generalized smoothness in the critical case
In: Journal of Fourier Analysis and Applications 17 (2011), p. 777--800
ISSN: 1069-5869
DOI: 10.1007/s00041-010-9155-0
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Trace operators in Besov and Triebel-Lizorkin spaces
In: Zeitschrift für Analysis und ihre Anwendungen 29 (2010), p. 275--302
ISSN: 0232-2064
DOI: 10.4171/ZAA/1409
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Besov spaces with positive smoothness (Dissertation, 2009)
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On dilation operators in Besov spaces
In: Revista Matematica Complutense 22 (2009), p. 111--128
ISSN: 1139-1138
DOI: 10.5209/rev_REMA.2009.v22.n1.16324
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Spaces of Sobolev type with positive smoothness on {$\Bbb R^n$}, embeddings and growth envelopes
In: Journal of Function Spaces and Applications 7 (2009), p. 251--288
ISSN: 0972-6802
DOI: 10.1155/2009/815676
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Besov spaces with positive smoothness on {$\Bbb R^n$}, embeddings and growth envelopes
In: Journal of Approximation Theory 161 (2009), p. 723--747
ISSN: 0021-9045
DOI: 10.1016/j.jat.2008.12.004
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On dilation operators in Triebel-Lizorkin spaces
In: Functiones et Approximatio, Commentarii Mathematici 41 (2009), p. 139--162
ISSN: 0208-6573
DOI: 10.7169/facm/1261157806
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Theses
- C. Schneider, ”Besov regularity of partial differential equations, and traces in function spaces”, Habilitation thesis, Philipps-University Marburg, 2020.
- C. Schneider, ”Besov spaces with positive smoothness”, PhD Thesis, University of Leipzig, 2009.
- C. Schneider, ”Growth envelopes in Sobolev spaces”, Diploma Thesis, Friedrich-Schiller-University Jena, 2006.