26 citations · 138 across the 26 of their papers we have counts for
13 papers · 1 filter
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…
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…
local smoothing estimates for the wave equation via -broad Fourier restriction
David Beltran, Olli Saari
We explore the connection between -broad Fourier restriction estimates and sharp regularity local smoothing estimates for the solutions of the wave equation in $\mathb…
Construction of a right inverse for the divergence in non-cylindrical time dependent domains
Olli Saari, Sebastian Schwarzacher
We construct a stable right inverse for the divergence operator in non-cylindrical domains in space-time. The domains are assumed to be Hölder regular in space and evolve continuou…
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…
A reverse Hölder inequality for the gradient of solutions to Trudinger's equation
Olli Saari, Sebastian Schwarzacher
We provide a higher integrability result for the gradient of positive solutions to Trudinger's equation (also known as the doubly non-linear equation) for the range $p\in [2,\infty…
The Brunn-Minkowski inequality and a Minkowski problem for -harmonic Green's function
Murat Akman, John Lewis, Olli Saari +1
In this article we study two classical problems in convex geometry associated to -harmonic PDEs, quasi-linear elliptic PDEs whose structure is modeled on the -Lapla…
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…
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…
Parabolic BMO and the forward-in-time maximal operator
Olli Saari
We study if the parabolic forward-in-time maximal operator is bounded on parabolic BMO. It turns out that for non-negative functions the answer is positive, but the behaviour of si…
Characterizations of interior polar sets for the degenerate p-parabolic equation
Benny Avelin, Olli Saari
This paper deals with different characterizations of sets of nonlinear parabolic capacity zero, with respect to the parabolic p-Laplace equation. Specifically we prove that certain…
Parabolic weighted norm inequalities and partial differential equations
Juha Kinnunen, Olli Saari
We investigate parabolic Muckenhoupt weights and functions of bounded mean oscillation (BMO) related to nonlinear parabolic partial differential equations. The main result gives a…
Parabolic BMO and global integrability of supersolutions to doubly nonlinear parabolic equations
Olli Saari
We prove that local and global parabolic BMO spaces are equal thus extending the classical result of Reimann and Rychener. Moreover, we show that functions in parabolic BMO are exp…