We prove local Lipschitz regularity for weak solutions to a parabolic orthotropic $p$-Laplacian-type equation in the Heisenberg group $\Hn$, for the range $2\leq p\leq4$.
This article is concerned with the unconditional well-posedness for the Kawahara equation on the real line and shows that this holds true for initial data in $L^2(\mathbb{R})$. This is achieved by applying an infinite iteration scheme of normal form reductions.
We prove the existence of a mild solution to the three dimensional incompressible stochastic magnetohydrodynamic equations in the whole space with the initial data which belong to the Sobolev spaces.
We establish a family of inequalities that allow one to estimate the $\mathrm{L}^{q}$-norm of a matrix-valued field by the $\mathrm{L}^{q}$-norm of an elliptic part and the $\mathrm{L}^{p}$-norm of the matrix-valued curl. This particularly extends previous work by Neff et al. and, as a main novelty, is applicable in the regime $p=1$.
Sebagai supervisor di sebuah sekolah, seorang kepala sekolah harus mampu melakukan pengawasan dan pengendalian untuk meningkatkan kinerja guru. Kegiatan pengawasan dan pengendalian merupakan tindakan preventiv atau pencegah agar guru lebih berhati-hati dan tidak melakukan penyimpangan dalam melaksanakan tugasnya sebagai pendidik. Penelitian ini mengungkap pelaksanaan supervisi yang dilakukan kepalas sekolah MIN Sukadamai Kota Banda Aceh terhadap kinerja guru. Setelah dilakukan penelitian ini, didapatkan hasil sebagai berikut: 1) focus kegiatan supervise yang dilakukan kepala sekolah dapat di identifikasikan ke dalam dua hal yaitu kegiatan supervise yang menyangkut administrasi guru dan kegiatan proses belajar mengajar. 2) kegiatan supervise sangat membantu guru dalam menyelesaikan masalah-masalah pendidikan yang dihadapi guru saat melakukan kegiatan pembelajaran, dan memotivasi guru untuk selalu meningkatkan pengetahuannya menjadi guru professional. 3) tumpang tindih kegiatan dan dana operasional menjadi hambatan kepala sekolah dalam melakukan supervise.
This study focuses on stakeholders and changing perspectives on a heritage site. The case study is an historic cemetery within a public state park that was the location of a Russian colony in northern California: Fort Ross State Historic Park. From 1990–1992, I excavated the cemetery at the Russian Colony Ross, which was in use from 1812–1841, and which included Russians, Native Alaskans, Native Americans, and combinations thereof. A total of 135 burials were excavated and reburied. Although the Russian Orthodox Church has clear requirements for funeral and burial, the specific location and extent of the cemetery were unknown. Examining the site from the perspective of different stakeholders and their agendas, this article explores the changing nature of a mortuary heritage site, as well as how different groups interpret and use the same site, how communities reacted to the excavation project, and how the project continues to have an impact on communities. Various stakeholders have used the cemetery in different ways to memorialize their own pasts and make claims in the present.
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 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.
This is the content of the talk the author gave in the section of partial differential equations at the International Congress of Chinese Mathematicians, 2013, Taipei.
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.
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.
We use a characterization of the fractional Laplacian as a Dirichlet to Neumann operator for an appropriate differential equation to study its obstacle problem in perforated domains.