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Variable Exponent Regularity via Muckenhoupt Condition
Daviti Adamadze, Anna Kh. Balci, Lars Diening
For the first time, we establish higher integrability of the gradient and local estimates of weak solutions to the -Laplacian without assuming -Hölder contin…
Nonlocal Meyers' Example
Anna Kh. Balci, Lars Diening, Moritz Kassmann +1
We present nonlocal variants of the famous Meyers' example of limited higher integrability and differentiability. In the limit we recover the standard Meyers' exampl…
Examples of -harmonic maps
Anna Balci, Linus Behn, Lars Diening +1
We construct explicit examples of -harmonic maps . These are more irregular than the previously known examples and thus provide new upper bounds…
Gradient estimates for parabolic nonlinear nonlocal equations
Lars Diening, Kyeongbae Kim, Ho-Sik Lee +1
The primary objective of this work is to establish pointwise gradient estimates for solutions to a class of parabolic nonlinear nonlocal measure data problems, expressed in terms o…
Nonlocal equations with degenerate weights
Linus Behn, Lars Diening, Jihoon Ok +1
We introduce fractional weighted Sobolev spaces with degenerate weights. For these spaces we provide embeddings and Poincaré inequalities. When the order of fractional differentiab…
Higher differentiability for the fractional -Laplacian
Lars Diening, Kyeongbae Kim, Ho-Sik Lee +1
In this work, we study the higher differentiability of solutions to the inhomogeneous fractional -Laplace equation under different regularity assumptions on the data. In the sup…
The De Giorgi method for local and nonlocal systems
Linus Behn, Lars Diening, Simon Nowak +1
We extend the De Giorgi iteration technique to the vectorial setting. For this we replace the usual scalar truncation operator by a vectorial shortening operator. As an application…
Nonlinear nonlocal potential theory at the gradient level
Lars Diening, Kyeongbae Kim, Ho-Sik Lee +1
The aim of this work is to establish numerous interrelated gradient estimates in the nonlinear nonlocal setting. First of all, we prove that weak solutions to a class of homogeneou…
Scalar minimizers with maximal singular sets and lack of Meyers property
Anna Balci, Lars Diening, Mikhail Surnachev
We present a general procedure to construct examples of convex scalar variational problems which admit a minimizers with large singular sets. The dimension of the set of singularit…
Global regularity for nonlinear systems with symmetric gradients
Linus Behn, Lars Diening
We study global regularity of nonlinear systems of partial differential equations depending on the symmetric part of the gradient with Dirichlet boundary conditions. These systems…