相关论文: Strong unique continuation and global regularity e…

In this paper, we extend the nontangential maximal function estimate obtained by C. Kenig, F. Lin and Z. Shen in \cite{KFS1} to the nonhomogeneous elliptic operators with rapidly oscillating periodic coefficients. The result relies on the…

We obtain a complete characterization of $L^p-L^q$ Carleman estimates with weight $e^{v\cdot x}$ for the polyharmonic operators. Our result extends the Carleman inequalities for the Laplacian due to Kenig--Ruiz--Sogge. Consequently, we…

We consider a first order operator with a periodic 3x3 matrix potential on the real line. This operator appears in the problem of the periodic vector NLS equation. The spectrum of the operator covers the real line, it is union of the…

We consider a classical shape optimization problem for the eigenvalues of elliptic operators with homogeneous boundary conditions on domains in the $N$-dimensional Euclidean space. We survey recent results concerning the analytic dependence…

The development of a nonlinear structural theory (model) for isotropic linear-elastic finite continua is the main objective of the study. To derive the theory, we used Taylor's multivariable expansion and Bubnov-Galerkin's weak formulation.…

In a refined Sobolev scale, we investigate an elliptic boundary-value problem with additional unknown functions in boundary conditions for which the maximum of orders of boundary operators is grater than or equal to the order of the…

This paper studies global a priori gradient estimates for divergence-type equations patterned over the $p$-Laplacian with first-order terms having polynomial growth with respect to the gradient, under suitable integrability assumptions on…

We provide a complete local well-posedness theory in $H^s$ based Sobolev spaces for the free boundary incompressible Euler equations with zero surface tension on a connected fluid domain. Our well-posedness theory includes: (i) Local…

We consider uniformly elliptic operators with Dirichlet or Neumann homogeneous boundary conditions on a domain $\Omega $ in ${\mathbb{R}}^N$. We consider deformations $\phi (\Omega)$ of $\Omega $ obtained by means of a locally Lipschitz…

This paper is concerned with a family of second-order elliptic systems in divergence form with rapidly oscillating periodic coefficients. We initiate the study of homogenization and boundary layers for Neumann problems with first-order…

We propose a complement to constitutive modeling that augments neural networks with material principles to capture anisotropy and inelasticity at finite strains. The key element is a dual potential that governs dissipation, consistently…

The pure traction problem of elasticity appears frequently in engineering applications, and its complexity stems from the fact that its solution is unique only up to (infinitesimal) rigid body motions. When finite elements are employed to…

We consider the Neumann problem in $C^2$ bounded domains for fully nonlinear second order operators which are elliptic, homogenous with lower order terms. Inspired by \cite{bnv}, we define the concept of principal eigenvalue and we…

This note introduces a class of nonlinear Neumann problems on balls expanding with the radii tending towards infinity. Performing singular perturbation arguments, we establish the corresponding concentration phenomenon and refined…

In this article we are interested in studying regularity up to the boundary for one-phase singularly perturbed fully nonlinear elliptic problems, associated to high energy activation potentials, namely $$ F(X, \nabla u^{\varepsilon}, D^2…

We investigate a smoothing property for strongly-continuous operator semigroups, akin to ultracontractivity in parabolic evolution equations. Specifically, we establish the stability of this property under certain relatively bounded…

We study an indefinite spectral problem for a second-order self-adjoint elliptic operator in an asymptotically thin cylinder. The operator coefficients and the spectral density function are assumed to be locally periodic in the axial…

We consider solutions to degenerate anisotropic elliptic equations in order to study their regularity. In particular we establish second-order estimates and enclose regularity results for the stress field. All our results are new even in…

We consider the weighted eigenvalue problem for a general non-local pseudo-differential operator, depending on a bounded weight function. For such problem, we prove that strict (decreasing) monotonicity of the eigenvalues with respect to…

Building on the foundation work of Brown, Milton and Torquato, we present a tractable approach to analyse the effective permittivity of anisotropic two-phase structures. This methodology accounts for successive dipolar interactions,…