31 citations · 127 across the 24 of their papers we have counts for
32 papers
Singular solutions to parabolic equations in one space dimension
Pascal Auscher, Moritz Egert, Benjamin W. Kosmala
We construct singular weak solutions to scalar, linear, uniformly parabolic equations with complex coefficients in one space dimension. Our examples show that the space-time integr…
The parabolic Dini- condition and absolute continuity of surface and caloric measure
Simon Bortz, Moritz Egert, Sandra Ferris +1
We show if is the graph of a parabolic Lipschitz function, then parabolic surface measure of is absolutely continuous with respect to its caloric meas…
bounds for parabolic Riesz transforms with rough coefficients: The case
Khalid Baadi, Moritz Egert, Benjamin W. Kosmala
We establish the first results on bounds for Riesz transforms associated with non-autonomous second order parabolic differential operators in divergence form with bo…
Meyers exponent rules the first-order approach to second-order elliptic boundary value problems
Pascal Auscher, Tim Böhnlein, Moritz Egert
The first-order approach to boundary value problems for second-order elliptic equations in divergence form with transversally independent complex coefficients in the upper half-spa…
A Note on Complex Interpolation of Quasi-Banach Function Spaces
Moritz Egert, Benjamin W. Kosmala
Kalton and Mitrea characterized complex interpolation spaces of quasi-Banach function spaces as Calderón products if both interpolants are separable. We show that one separability…
A stability result for parabolic measures of operators with singular drifts
Simon Bortz, Moritz Egert, Olli Saari
We study the operator \[ \partial_t - \text{div} A \nabla + B \cdot \nabla \] in parabolic upper-half-space, where is an elliptic matrix satisfying an oscillation condition and…
Bounded functional calculus for divergence form operators with dynamical boundary conditions
Tim Böhnlein, Moritz Egert, Joachim Rehberg
We consider divergence form operators with complex coefficients on an open subset of Euclidean space. Boundary conditions in the corresponding parabolic problem are dynamical, that…
Gaussian estimates vs. elliptic regularity on open sets
Tim Böhnlein, Simone Ciani, Moritz Egert
Given an elliptic operator subject to mixed boundary conditions on an open subset of , we study the relation between Gaussian poi…
Explicit improvements for -estimates related to elliptic systems
Tim Böhnlein, Moritz Egert
We give a simple argument to obtain -boundedness for heat semigroups associated to uniformly strongly elliptic systems on by using Stein interpolation…
A universal variational framework for parabolic equations and systems
Pascal Auscher, Moritz Egert
We propose a variational approach to solve Cauchy problems for parabolic equations and systems independently of regularity theory for solutions. This produces a universal and conce…
The Kato square root problem for weighted parabolic operators
Alireza Ataei, Moritz Egert, Kaj Nyström
We give a simplified and direct proof of the Kato square root estimate for parabolic operators with elliptic part in divergence form and coefficients possibly depending on space an…
Carleson Conditions for Weights: The quantitative small constant case
Simon Bortz, Moritz Egert, Olli Saari
We investigate the small constant case of a characterization of weights due to Fefferman, Kenig and Pipher. In their work, Fefferman, Kenig and Pipher bound the logarith…
Hardy spaces for boundary value problems of elliptic systems with block structure
Pascal Auscher, Moritz Egert
We present recent results on elliptic boundary value problems where the theory of Hardy spaces associated with operators plays a key role.
Boundary value problems and Hardy spaces for elliptic systems with block structure
Pascal Auscher, Moritz Egert
For elliptic systems with block structure in the upper half-space and t-independent coefficients, we settle the study of boundary value problems by proving compatible well-posednes…
Note on time-regularity for weak solutions to parabolic systems of p-Laplace type
Simon Bortz, Moritz Egert, Olli Saari
We show that local weak solutions to parabolic systems of p-Laplace type are H{ö}lder continuous in time with values in a spatial Lebesgue space and H{ö}lder continuous on almost e…
Sobolev contractivity of gradient flow maximal functions
Simon Bortz, Moritz Egert, Olli Saari
We prove that the energy dissipation property of gradient flows extends to the semigroup maximal operators in various settings. In particular, we show that the vertical maximal fun…
On p-elliptic divergence form operators and holomorphic semigroups
Moritz Egert
Second order divergence form operators are studied on an open set with various boundary conditions. It is shown that the p-ellipticity condition of Carbonaro-Dragicevic and Dindos-…
Interpolation theory for Sobolev functions with partially vanishing trace on irregular open sets
Sebastian Bechtel, Moritz Egert
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…
Lp-estimates for the square root of elliptic systems with mixed boundary conditions
Moritz Egert
This article focuses on Lp-estimates for the square root of elliptic systems of second order in divergence form on a bounded domain. We treat complex bounded measurable coefficient…
Non-local self-improving properties: A functional analytic approach
Pascal Auscher, Simon Bortz, Moritz Egert +1
A functional analytic approach to obtaining self-improving properties of solutions to linear non-local elliptic equations is presented. It yields conceptually simple and very short…
Non-local Gehring lemmas in spaces of homogeneous type and applications
Pascal Auscher, Simon Bortz, Moritz Egert +1
We prove a self-improving property for reverse H{ö}lder inequalities with non-local right hand side. We attempt to cover all the most important situations that one encounters when…
On regularity of weak solutions to linear parabolic systems with measurable coefficients
Pascal Auscher, Simon Bortz, Moritz Egert +1
We establish a new regularity property for weak solutions of parabolic systems with coefficients depending measurably on time as well as on all spatial variables. Namely, weak solu…
On uniqueness results for Dirichlet problems of elliptic systems without DeGiorgi-Nash-Moser regularity
Pascal Auscher, Moritz Egert
We study uniqueness of Dirichlet problems of second order divergence-form elliptic systems with transversally independent coefficients on the upper half-space in absence of regular…
The Dirichlet problem for second order parabolic operators in divergence form
Pascal Auscher, Moritz Egert, Kaj Nyström
We study parabolic operators H = t -- div ,x A(x, t) ,x in the parabolic upper half space R n+2 + = {(, x, t) : > 0}. We assume that the coefficients…