The virtual element method is well suited to the formulation of arbitrarily regular Galerkin
approximations of elliptic partial differential equations of order 2 p 1, for any integer p 1≥ 1 …

Advances in microfabrication technology have enabled micromechanical systems (MEMS)
to become a core component in a manifold of applications. For many of these applications …

In recent work it has been established that deep neural networks (DNNs) are capable of
approximating solutions to a large class of parabolic partial differential equations without …

This article investigates nonlocal, quasilinear generalizations of the classical biharmonic
operator (-Δ) 2. These fractional p-biharmonic operators appear naturally in the variational …

In this work, we exploit the capability of virtual element methods in accommodating
approximation spaces featuring high-order continuity to numerically approximate differential …

Abstract We investigate the Bi-Laplacian with Wentzell boundary conditions in a bounded
domain Ω ⊆ R^ d Ω⊆ R d with Lipschitz boundary Γ Γ. More precisely, using form methods …

In the past fifteen years mathematical models for microelectromechanical systems (MEMS)
have been the subject of several studies, in particular due to the interesting qualitative …

In this paper, we prove an existence result of nontrivial solutions for the problem Δ2u±Δpu= f
(u) inΩ, andu= Δu= 0on∂ Ω, $${\Delta} & amp;# x0005E; 2u\pm {\Delta} _pu& …

The main purpose of this paper is to establish the existence, nonexistence and symmetry of
nontrivial solutions to the higher order Brezis-Nirenberg problems associated with the GJMS …

In this article, we study an inverse problem with local data for a linear polyharmonic operator
with several lower order tensorial perturbations. We consider our domain to have an …