Results 51 to 60 of about 1,966 (104)

Nonlinear elliptic equations with high order singularities [PDF]

, 2016
We study non-variational degenerate elliptic equations with high order singular structures. No boundary data are imposed and singularities occur along an {\it a priori} unknown interior region. We prove that positive solutions have a universal modulus of
Teixeira, Eduardo V.
core  

H\"older regularity for Maxwell's equations under minimal assumptions on the coefficients

, 2018
We prove global H\"older regularity for the solutions to the time-harmonic anisotropic Maxwell's equations, under the assumptions of H\"older continuous coefficients. The regularity hypotheses on the coefficients are minimal. The same estimates hold also
Alberti, Giovanni S.
core   +1 more source

Double-phase parabolic equations with variable growth and nonlinear sources

Advances in Nonlinear Analysis, 2022
We study the homogeneous Dirichlet problem for the parabolic equations ut−div(A(z,∣∇u∣)∇u)=F(z,u,∇u),z=(x,t)∈Ω×(0,T),{u}_{t}-{\rm{div}}\left({\mathcal{A}}\left(z,| \nabla u| )\nabla u)=F\left(z,u,\nabla u),\hspace{1.0em}z=\left(x,t)\in \Omega \times ...
Arora Rakesh, Shmarev Sergey
doaj   +1 more source

Solvability and microlocal analysis of the fractional Eringen wave equation

, 2017
We discuss unique existence and microlocal regularity properties of Sobolev space solutions to the fractional Eringen wave equation, initially given in the form of a system of equations in which the classical non-local Eringen constitutive equation is ...
Hörmann, Günther, Oparnica, Ljubica, Zorica, Dušan   +2 more
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The exterior Dirichlet problem for the homogeneous complex k-Hessian equation

Advanced Nonlinear Studies, 2023
In this article, we consider the homogeneous complex kk-Hessian equation in an exterior domain Cn⧹Ω{{\mathbb{C}}}^{n}\setminus \Omega . We prove the existence and uniqueness of the C1,1{C}^{1,1} solution by constructing approximating solutions.
Gao Zhenghuan, Ma Xinan, Zhang Dekai
doaj   +1 more source

Non-oriented solutions of the eikonal equation [PDF]

, 2008
We study a new formulation for the eikonal equation |grad u| =1 on a bounded subset of R^2. Instead of a vector field grad u, we consider a field P of orthogonal projections on 1-dimensional subspaces, with div P in L^2. We prove existence and uniqueness
Peletier, Mark A., Veneroni, Marco
core   +1 more source

Non-homogeneous fully nonlinear contracting flows of convex hypersurfaces

Advanced Nonlinear Studies
We consider a general class of non-homogeneous contracting flows of convex hypersurfaces in Rn+1 ${\mathbb{R}}^{n+1}$ , and prove the existence and regularity of the flow before extincting to a point in finite time.
Guan Pengfei, Huang Jiuzhou, Liu Jiawei
doaj   +1 more source

Gradient estimate of a variable power for nonlinear elliptic equations with Orlicz growth

Advances in Nonlinear Analysis, 2020
In this paper, we prove a global Calderón-Zygmund type estimate in the framework of Lorentz spaces for a variable power of the gradients to the zero-Dirichlet problem of general nonlinear elliptic equations with the nonlinearities satisfying Orlicz ...
Liang Shuang, Zheng Shenzhou
doaj   +1 more source

Local Elliptic Regularity for the Dirichlet Fractional Laplacian

Advanced Nonlinear Studies, 2017
We prove the Wloc2⁢s,p${W_{{\mathrm{loc}}}^{2s,p}}$ local elliptic regularity of weak solutions to the Dirichlet problem associated with the fractional Laplacian on an arbitrary bounded open set of ℝN${\mathbb{R}^{N}}$. The key tool consists in analyzing
Biccari Umberto, Warma Mahamadi, Zuazua Enrique   +2 more
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New Results About the Lambda Constant and Ground States of the 𝑊-Functional

Advanced Nonlinear Studies, 2020
In this paper, we study properties of the lambda constants and the existence of ground states of Perelman’s famous W-functional from a variational formulation. We have two kinds of results.
Ma Li
doaj   +1 more source