Results 61 to 70 of about 89,789 (287)

Fine topology and quasilinear elliptic equations [PDF]

Annales de l'Institut Fourier, 1989
It is shown that the (1,p)-fine topology defined via a Wiener criterion is the coarsest topology making all supersolutions to the p-Laplace equation div (|∇u|p-2∇u)=0continuous. Fine limits of quasiregular and BLD mappings are also studied.
Heinonen, J., Kilpeläinen, T., Martio, O.   +2 more
openaire   +2 more sources

A Microfluidic Platform for Actin‐Based Membrane Remodeling Reveals the Stabilizing Role of Branched Actin Networks on Lipid Microdomains

Small Science, Volume 5, Issue 10, October 2025.
A microfluidic assay to study actin‐driven shape changes of giant unilamellar vesicles (GUVs) is developed. This system enables high‐throughput analysis of membrane remodeling and reveals how actin networks and lipid domains influence each other. It offers a powerful tool to dissect membrane deformation mechanisms in controlled environments. Cell shape
Lixin Huang, Rogério Lopes Dos Santos, Sid Labdi, Guillaume Lamour, Olek Maciejak, Michel Malo, John Manzi, Martin Lenz, Jacques Fattaccioli, Clément Campillo   +9 more
wiley   +1 more source

The Existence and Uniqueness Result for a Relativistic Nonlinear Schrödinger Equation

Abstract and Applied Analysis, 2014
We study the existence and uniqueness of positive solutions for a class of quasilinear elliptic equations. This model has been proposed in the self-channeling of a high-power ultrashort laser in matter.
Yongkuan Cheng, Jun Yang
doaj   +1 more source

Brezis–Nirenberg type results for the anisotropic p$p$‐Laplacian

Journal of the London Mathematical Society, Volume 112, Issue 4, October 2025.
Abstract In this paper, we consider a quasilinear elliptic and critical problem with Dirichlet boundary conditions in presence of the anisotropic p$p$‐Laplacian. The critical exponent is the usual p★$p^{\star }$ such that the embedding W01,p(Ω)⊂Lp★(Ω)$W^{1,p}_{0}(\Omega) \subset L^{p^{\star }}(\Omega)$ is not compact.
Stefano Biagi, Francesco Esposito, Alberto Roncoroni, Eugenio Vecchi   +3 more
wiley   +1 more source

Solutions of anisotropic elliptic equations in unbounded domains

Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2013
In the paper the Dirichlet problem for an anisotropic quasilinear elliptic equations of the second order is considered. The upper estimates for the generalized solution of this Dirichlet problem are received, the closeness is proved for the isotropic ...
Larisa Mikhailovna Kozhevnikova, Anna Alexandrovna Khadzhi   +1 more
doaj   +1 more source

Quasilinear degenerate elliptic equation with absorption term

Nonlinear Analysis: Theory, Methods & Applications, 1999
The author studies the Dirichlet problem for \(p\)-harmonic operators \[ L_pu=-\text{div} (A(x)|\nabla u|^{p-2}\nabla u) \] with absorption term \[ L_pu+B(x)Q(u)= f(x)\quad \text{in } \Omega,\qquad u=0\quad \text{on } \partial\Omega. \] Here \(B(x)\) is a nonnegative function on \(\Omega\) and \(Q(t)\) is a continuous and strictly monotone increasing ...
openaire   +3 more sources

Quasilinear elliptic equations via perturbation method [PDF]

Proceedings of the American Mathematical Society, 2012
The paper is concerned with the existence and multiplicity of solutions for quasilinear equations of the form \[ \begin{cases} \sum _ {i,j=1}^ND_j( a_{ij}(x,u) D_iu) & \\ \qquad-\frac12 \sum _{i,j=1}^N D_sa_{ij}(x,u) D_iu D_ju + f(x,u)=0& \mathrm{in}\,\, \Omega ,\\ u=0 & \mathrm{on}\,\, \partial \Omega \end{cases} \tag{1} \] where \(D_i= \partial ...
Liu, Xiang-Qing, Liu, Jia-Quan, Wang, Zhi-Qiang   +2 more
openaire   +2 more sources

Second‐order regularity for degenerate p$p$‐Laplace type equations with log‐concave weights

Journal of the London Mathematical Society, Volume 112, Issue 3, September 2025.
Abstract We consider weighted p$p$‐Laplace type equations with homogeneous Neumann boundary conditions in convex domains, where the weight is a log‐concave function which may degenerate at the boundary. In the case of bounded domains, we provide sharp global second‐order estimates. For unbounded domains, we prove local estimates at the boundary.
Carlo Alberto Antonini, Giulio Ciraolo, Francesco Pagliarin   +2 more
wiley   +1 more source

Solvability of quasilinear elliptic equations with strong dependence on the gradient

Abstract and Applied Analysis, 2000
We study the problem of existence of positive, spherically symmetric strong solutions of quasilinear elliptic equations involving p-Laplacian in the ball. We allow simultaneous strong dependence of the right-hand side on both the unknown function and its
Darko Žubrinić
doaj   +1 more source

Arithmetic three-spheres theorems for quasilinear Riccati type inequalities [PDF]

, 2015
We consider arithmetic three-spheres inequalities to solutions of certain second order quasilinear elliptic differential equations and inequalities with a Riccati-type drift term.Comment: to appear in Journal d'Analyse Math ...
Granlund, Seppo, Marola, Niko
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