相关论文: Gradient estimates for the $p$-Laplacian perfect c…
This paper concerns optimal gradient estimates of solutions for the perfect conductivity problem with closely spaced interfacial boundaries. The problem arises from composite material. Our estimates exhibit different blow up rates of the…
In this paper, we study the perfect and the insulated conductivity problems with multiple inclusions imbedded in a bounded domain in $\mathbb{R}^n, n\ge 2$. For these two extreme cases of the conductivity problems, the gradients of their…
We study the insulated conductivity problem with inclusions embedded in a bounded domain in $\mathbb{R}^n$. It was known that in the setting of strictly convex inclusions, the gradient of solutions may blow up as the distance between…
We study the perfect conductivity problem with closely spaced perfect conductors embedded in a homogeneous matrix where the current-electric field relation is the power law $J=\sigma|E|^{p-2}E$. The gradient of solutions may be arbitrarily…
In high-contrast composite materials, the electric field concentration is a common phenomenon when two inclusions are close to touch. It is important from an engineering point of view to study the dependence of the electric field on the…
This paper studies field concentration between two nearly touching conductors separated by imperfect low-conductivity interfaces, modeled by Robin boundary conditions. It is known that for any sufficiently small interfacial bonding…
When a convex perfectly conducting inclusion is closely spaced to the boundary of the matrix domain, a bigger convex domain containing the inclusion, the electric field can be arbitrary large. We establish both the pointwise upper bound and…
We study the perfect conductivity problem when two perfectly conducting inclusions are closely located to each other in an anisotropic background medium. We establish optimal upper and lower gradient bounds for the solution in any dimension…
We study the insulated conductivity problem with inclusions embedded in a bounded domain in $\mathbb R^n$, for $n \ge 3$. The gradient of solutions may blow up as $\varepsilon$, the distance between inclusions, approaches to $0$. We…
We study the field concentration phenomenon between two closely spaced perfect conductors with imperfect bonding interfaces of low conductivity type. The boundary condition on these interfaces is given by a Robin-type boundary condition. We…
We study the insulated conductivity problem which involves two adjacent convex insulators embedded in a bounded domain. It is known that the gradient of solutions may blow up as the distance between the two inclusions tends to zero.…
In the perfect conductivity problem, it is interesting to study whether the electric field can become arbitrarily large or not, in a narrow region between two adjacent perfectly conducting inclusions. In this paper, we show that the…
When inclusions with extreme conductivity (insulator or perfect conductor) are closely located, the gradient of the solution to the conductivity equation can be arbitrarily large. And computation of the gradient is extremely challenging due…
We consider an insulated conductivity model with two neighboring inclusions of $m$-convex shapes in $\mathbb{R}^{d}$ when $m\geq2$ and $d\geq3$. We establish the pointwise gradient estimates for the insulated conductivity problem and…
We study the insulated conductivity problem with closely spaced insulators embedded in a homogeneous matrix where the current-electric field relation is the power law $J = |E|^{p-2}E$. The gradient of solutions may blow up as $\varepsilon$,…
We study a class of second-order elliptic equations of divergence form, with discontinuous coefficients and data, which models the conductivity problem in composite materials. We establish optimal gradient estimates by showing the explicit…
We study the stress concentration, which is the gradient of the solution, when two smooth inclusions are closely located in a possibly anisotropic medium. The governing equation may be degenerate of $p-$Laplace type, with $1<p \leq N$. We…
We study the gradient and higher order derivative estimates for the transmission problem in the presence of closely located inclusions. We show that in two dimensions, when relative conductivities of circular inclusions have different…
We consider a gradient estimate for a conductivity problem whose inclusions are two neighboring insulators in three dimensions. When inclusions with an extreme conductivity (insulators or perfect conductors) are closely located, the…
In this paper we study the boundary gradient estimate of the solution to the insulated conductivity problem with the Neumann boundary data when a convex insulating inclusion approaches the boundary of the matrix domain. The gradient of…