Related papers: Weak uniqueness and partial regularity for the com…

We prove the partial regularity of the boundary suitable weak solutions to the MHD system near the plane part of the boundary.

First, a new sufficient condition for uniqueness of weak solutions is proved for the system of 2D viscous Primitive Equations. Second, global existence and uniqueness are established for several classes of weak solutions with partial…

The existence of minimizers in the fractional isoperimetric problem with multiple volume constraints is proved, together with a partial regularity result.

In the first part of this doctoral thesis we develop a regularity theory for a polyconvex functional in compressible elasticity. In the second part, we will concentrate on uniqueness questions in various situations of finite elasticity.…

We study the regularity of minimizers to the composite membrane problem in the plane (ie given a domain omega and a positive number A, smaller than the measure of omega, minimize the first Dirichlet eigenvalue for the Schrodinger operator…

In this article, the uniqueness of weak solutions to the continuous coagulation and multiple fragmentation equation is proved for a large range of unbounded coagulation and multiple fragmentation kernels. The multiple fragmentation kernels…

This is a continuation of the paper 'Symmetry breaking and other phenomena in the optimization of eigenvalues for composite membranes' by S. Chanillo, D. Grieser, M. Imai, K. Kurata, and I. Ohnishi. Again, we consider the following…

In this paper, we mainly introduce a general method to study the existence and uniqueness of solution of free boundary problems with partially degenerate diffusion.

We consider a nematic liquid crystal flow with partially free boundary in a smooth bounded domain in $\mathbb{R}^2$. We prove regularity estimates and the global existence of weak solutions enjoying partial regularity properties, and a…

We study the regularity properties of a weak solution to the boundary value problem for the equation $-\Delta \rho +a u=f$ in a bounded domain $\Omega\subset \mathbb{R}^N$, where $\rho=e^{-\mbox{div}\left(|\nabla u|^{p-2}\nabla…

We establish the density of the partial regularity result in the class of continuous viscosity solutions. Given a fully nonlinear equation, we prove the existence of a sequence entitled to the partial regularity result, approximating its…

We consider smooth bounded surfaces with a smooth boundary and a prescribed background metric g_0. We now consider all metrics g conformal to g_0 which have a prescribed volume M. We now minimize the first eigenvalue of the Laplace operator…

We investigate a PDE-constrained optimization problem, with an intuitive interpretation in terms of the design of robust membranes made out of an arbitrary number of different materials. We prove existence and uniqueness of solutions for…

In this paper, we study the boundary pointwise regularity for the divergence form elliptic boundary problem on domains with rough boundaries, specifically uniform domains. In general, it is not straightforward to define weak solutions for…

In this article, we investigate some isoperimetric-type inequalities related to the first eigenvalue of the fractional composite membrane problem. First, we establish an analogue of the renowned Faber-Krahn inequality for the fractional…

We study a class of semilinear free boundary problems in which admissible functions $u$ have a topological constraint, or spanning condition, on their 1-level set. This constraint forces $\{u=1\}$, which is the free boundary, to behave like…

We prove some variational analysis of regularity and weak convergence of nonlocal variational principle.

We will give some regularity results about fractional diffusion-wave equations.

We survey a variety of results about partially isometric matrices. We focus primarily on results that are distinctly finite-dimensional. For example, we cover a recent solution to the similarity problem for partial isometries. We also…

We present several examples of fundamental problems involving weak continuity and compactness for nonlinear partial differential equations, in which compensated compactness and related ideas have played a significant role. We first focus on…