L$^2$ well-posedness of boundary value problems for parabolic systems with measurable coefficients

Autor: Pascal Auscher, Kaj Nyström, Moritz Egert

Publikováno v: J. Eur. Math. Soc. (JEMS) 6
J. Eur. Math. Soc. (JEMS) 6, 2020, 22 (9), pp.2943--3058
Journal of the European Mathematical Society
Journal of the European Mathematical Society, European Mathematical Society, 2020, 22 (9), pp.2943-3058. ⟨10.4171/JEMS/980⟩

We prove the first positive results concerning boundary value problems in the upper half-space of second order parabolic systems only assuming measurability and some transversal regularity in the coefficients of the elliptic part. To do so, we introd

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0fe8c82be0f01d61b3d4b9064aac1f1d
https://doi.org/10.4171/jems/980

Non-local Gehring Lemmas in Spaces of Homogeneous Type and Applications

Autor: Simon Bortz, Moritz Egert, Pascal Auscher, Olli Saari

Publikováno v: Journal of Geometric Analysis
Journal of Geometric Analysis, 2020, 30 (4), pp.3760--3705. ⟨10.1007/s12220-019-00217-z⟩

We prove a self-improving property for reverse H{\"o}lder inequalities with non-local right hand side. We attempt to cover all the most important situations that one encounters when studying elliptic and parabolic partial differential equations as we

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::49ad3584799fe5a4376ee2e98f902225
https://doi.org/10.1007/s12220-019-00217-z

Note on time-regularity for weak solutions to parabolic systems of p-Laplace type

Autor: Moritz Egert, Simon Bortz, Olli Saari

Publikováno v: Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society, American Mathematical Society, 2021, 149 (4), pp.1677-1685. ⟨10.1090/proc/15344⟩

We show that local weak solutions to parabolic systems of p-Laplace type are H{\"o}lder continuous in time with values in a spatial Lebesgue space and H{\"o}lder continuous on almost every time line. We provide an elementary and self-contained proof

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3c01bd0be7a7269afb63b9b968331a53
https://hal.archives-ouvertes.fr/hal-02412580v2/file/BES2-revison.pdf

Hardy spaces for boundary value problems of elliptic systems with block structure

Autor: Pascal Auscher, Moritz Egert

Publikováno v: The Journal of Geometric Analysis
The Journal of Geometric Analysis, Springer, 2021, ⟨10.1007/s12220-021-00608-1⟩

We present recent results on elliptic boundary value problems where the theory of Hardy spaces associated with operators plays a key role.
Comment: Survey article in the honor of Guido Weiss' ninetieth birthday. Upload of the published version.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4b9a73d282c8c5cbecf4225261129f4c

Interpolation theory for Sobolev functions with partially vanishing trace on irregular open sets

Autor: Moritz Egert, Sebastian Bechtel

Publikováno v: Journal of Fourier Analysis and Applications
Journal of Fourier Analysis and Applications, Springer Verlag, 2019, 25 (5), pp.2733-2781. ⟨10.1007/s00041-019-09681-1⟩

A full interpolation theory for Sobolev functions with smoothness between 0 and 1 and vanishing trace on a part of the boundary of an open set is established. Geometric assumptions are of mostly measure theoretic nature and reach beyond Lipschitz reg

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9109b19ff8f389018ecb0727ee3051df
https://hal.archives-ouvertes.fr/hal-01830708v3/file/Interpolation.pdf