We prove local Lipschitz regularity for weak solutions to a parabolic orthotropic $p$-Laplacian-type equation in the Heisenberg group $\Hn$, for the range $2\leq p\leq4$.
Cerina Chhuon, Luis Vicente Herrera-Marcos, Shao-Yu Zhang
et al.
Focal and segmental glomerulosclerosis (FSGS) is a severe form of idiopathic nephrotic syndrome (INS), a glomerulopathy of presumably immune origin that is attributed to extrarenal pathogenic circulating factors. The recurrence of FSGS (rFSGS) after transplant occurs in 30% to 50% of cases. The direct analysis of patient plasma proteome has scarcely been addressed to date, mainly due to the methodological difficulties associated with plasma complexity and dynamic range. In this study, first, we compared different methods of plasma preparation, second, we compared the plasma proteomes of rFSGS and controls using two preparation methods, and third, we analyzed the early proximal signaling events in podocytes subjected to patient plasma, through a combination of phosphoproteomics and lipid-raft proteomics (raftomics). By combining immunodepletion and high pH fractionation, we performed a differential proteomic analysis of soluble plasma proteins and of extracellular vesicles (EV) obtained from healthy controls, non-INS patient controls, and rFSGS patients (n = 4). In both the soluble- and the EV-protein sets from the rFSGS patients, we found a statistically significant increase in a cluster of proteins involved in neutrophil degranulation. A group of lipid-binding proteins, generally associated with lipoproteins, was found to be decreased in the soluble set from the rFSGS patients. In addition, three amino acid transporters involved in mTORC1 activation were found to be significantly increased in the EV from the rFSGS. Next, we incubated human podocytes for 30 min with 10% plasma from both groups of patients. The phosphoproteomics and raftomics of the podocytes revealed profound differences in the proteins involved in the mTOR pathway, in autophagy, and in cytoskeleton organization. We analyzed the correlation between the abundance of plasma and plasma-regulated podocyte proteins. The observed changes highlight some of the mechanisms involved in FSGS recurrence and could be used as specific early markers of circulating-factor activity in podocytes.
In this paper, we investigate the 3D inhomogeneous Navier-Stokes flows with vacuum, and obtain regularity criteria and Liouville type theorems in the Lorentz space if a smooth solution $(ρ, \mathbf{u})$ satisfies suitable conditions.
We prove sharp reverse Hölder inequalities for minima of multi-phase variational integrals and apply them to Calderón-Zygmund estimates for nonhomogeneous problems.
The aim of this article is to study the noncontrollability of the heat equation with double singular potential at an interior point and on the boundary of the domain.
We construct traveling wave solutions to the 3d Euler equations by axisymmetric Beltrami fields with a non-constant proportionality factor. They form a vortex ring with nested invariant tori consisting of level sets of the proportionality factor.
The mixed problem for a degenerate high order equation with a fractional derivative in a rectangular domain is considered in the article. The existence of a solution and its uniqueness are shown by the spectral method.
The problem we consider is given a mixed model $F(γ) \rightarrow γ\rightarrow \tildeγ$ and a potential $\widehat{V}$ such that $\log \widehat{V} \in L^{1}$, to determine a movement $U$ such that $F(U γ)=F(γ) + \widehat{V}$.
We present a proof of the $C^1$ regularity of $p$-orthotropic functions in the plane for $1<p<2$, based on the monotonicity of the derivatives. Moreover we achieve an explicit logarithmic modulus of continuity.
We study a general nonlinear elliptic equation in the Orlicz setting with data not belonging to the dual of the energy space. We provide several Lorentz-type and Morrey-type estimates for the gradients of solutions under various conditions on the data.
The present paper aims to generalize the Schauder estimate for a class of higher-order hypo-elliptic operators. The results in the present paper apply to parabolic equations of higher order and, for example, operators like $\partial_t^2-\partial_x^3$. Generalization to systems is also directly obtained.
Alexander Grebhahn, Carmen Rodrigo, Norbert Siegmund
et al.
SummaryMultigrid methods are among the most efficient algorithms for solving discretized partial differential equations. Typically, a multigrid system offers various configuration options to tune performance for different applications and hardware platforms. However, knowing the best performing configuration in advance is difficult, because measuring all multigrid system variants is costly. Instead of direct measurements, we use machine learning to predict the performance of the variants. Selecting a representative set of configurations for learning is nontrivial, although, but key to prediction accuracy. We investigate different sampling strategies to determine the tradeoff between accuracy and measurement effort. In a nutshell, we learn a performance‐influence model that captures the influences of configuration options and their interactions on the time to perform a multigrid iteration and relate this to existing domain knowledge. In an experiment on a multigrid system working on triangular grids, we found that combining pair‐wise sampling with the D‐Optimal experimental design for selecting a learning set yields the most accurate predictions. After measuring less than 1 % of all variants, we were able to predict the performance of all variants with an accuracy of 95.9 %. Furthermore, we were able to verify almost all knowledge on the performance behavior of multigrid methods provided by 2 experts.
We prove that that the 1-Riesz capacity satisfi es a Brunn-Minkowski inequality, and that the capacitary function of the 1/2-Laplacian is level set convex.
We consider a generalisation to quasilinear systems of the matched microstructure model. The proof of well posedness in a strong Sobolev setting is based on an approach via maximal regularity.
In this paper we use the method of matched asymptotic expansions in order to obtain a geometric motion as the singular limit of a nonlinear fourth order inhomogeneous equation.
Uwe Reusch, Olaf Bernhard, Ulrich Koszinowski
et al.
Heterotetrameric adaptor‐protein complexes AP‐1A and AP‐3A mediate protein sorting in post‐Golgi vesicular transport. AP‐1A and AP‐3A have been localized to the trans‐Golgi network, indicating a function in protein sorting at this compartment. AP‐3A appears to mediate trans‐Golgi network‐to‐lysosome and also endosome‐to‐lysosome protein sorting. AP‐1A is thought to be required for both trans‐Golgi network‐to‐endosome transport and endosome‐to‐trans‐Golgi network transport. However, the recent discovery of a role for monomeric GGA (Golgi localized γ‐ear containing, ARF binding protein) adaptor proteins in trans‐Golgi network to endosome protein transport has brought into question the long‐discussed trans‐Golgi network‐to‐endosome sorting function of AP‐1A. Murine cytomegalovirus gp48 contains an unusual di‐leucine‐based lysosome sorting signal motif and mediates lysosomal sorting of gp48/major histocompatibility complex class I receptor complexes, preventing exposure of major histocompatibility complex class I at the plasma membrane. We analyzed lysosomal sorting of gp48/major histocompatibility complex class I receptor complexes in cell lines deficient for AP‐1A, AP‐3A and both, to determine their sorting functions. We find that AP1‐A and AP3‐A mediate distinct and sequential steps in the lysosomal sorting. Both sorting functions are required to prevent MHC class I exposure at the plasma membrane at steady‐state.
We use spectral theory to produce embeddings of distributions in the algebras of generalized functions on a closed Riemannian manifold. These embeddings are invariant under isometries and preserve the singularity structure of the distributions.