Related papers: Detecting ill posed boundary conditions in General…
Perturbed stationary axisymmetric isolated bodies, e.g. stars, represented by a matter-filled interior and an asymptotically flat vacuum exterior joined at a surface where the Darmois matching conditions are satisfied, are considered. The…
Many evolution problems in physics are described by partial differential equations on an infinite domain; therefore, one is interested in the solutions to such problems for a given initial dataset. A prominent example is the binary black…
In this paper, we investigate the well-posedness theory for the MHD boundary layer system in two-dimensional space. The boundary layer equations are governed by the Prandtl type equations that are derived from the full incompressible MHD…
Consider $M$, a bounded domain in ${\mathbb R}^d$, which is a Riemanian manifold with piecewise smooth boundary and suppose that the billiard associated to the geodesic flow reflecting on the boundary acording to the laws of geometric…
We study an inhomogeneous Neumann boundary value problem for functions of least gradient on bounded domains in metric spaces that are equipped with a doubling measure and support a Poincar\'e inequality. We show that solutions exist under…
We establish boundary estimates for non-negative solutions to the p-parabolic equation in the degenerate range $p>2$. Our main results include new parabolic intrinsic Harnack chains in cylindrical NTA-domains together with sharp boundary…
We study boundary regularity at the infinity point $\boldsymbol{\infty}$ for nonlinear elliptic equations of $p$-Laplace type in unbounded open sets $\Omega \subset \mathbf{R}^n$. We consider the case $p \ge n \ge 2$ and characterize the…
We study the boundary regularity properties and derive a priori pointwise supremum estimates of weak solutions and their derivatives in terms of suitable weighted $L^2$-norms for a class of degenerate parabolic equations that satisfy…
Motivated by an analysis on the well-posedness of the initial boundary value problem for the motion of an inextensible hanging string, we first consider an initial boundary value problem for one-dimensional degenerate hyperbolic systems…
Two problems concerning asymptotically hyperbolic manifolds with an inner boundary are studied. First, we study scalar curvature presciption with either Dirichlet or mean curvature prescription interior boundary condition. Then we apply…
A new representation of the Einstein evolution equations is presented that is first order, linearly degenerate, and symmetric hyperbolic. This new system uses the generalized harmonic method to specify the coordinates, and exponentially…
On a closed Riemannian manifold, we construct a family of intrinsic Gaussian noises indexed by a regularity parameter $\alpha\geq0$ to study the well-posedness of the parabolic Anderson model. We show that with rough initial conditions, the…
On a class of four-dimensional Lifshitz spacetimes with critical exponent $z=2$, including a hyperbolic and a spherical Lifshitz topological black hole, we consider a real Klein-Gordon field. Using a mode-decomposition, we split the…
We investigate local well-posedness of the initial value problem for Lovelock and Horndeski theories of gravity. A necessary condition for local well-posedness is strong hyperbolicity of the equations of motion. Even weak hyperbolicity can…
We consider a mixed type boundary value problem for a class of degenerate parabolic-hyperbolic equations. Namely, we consider a Cartesian product domain and split its boundary into two parts. In one of them we impose a Dirichlet boundary…
Periodic boundary conditions are not always used in the study of disordered systems, but it can be advantageous to apply them to mimick thermodynamically large systems. In this case, polarization and its cumulants can not be obtained…
In this article, we consider Einstein-type manifolds with boundary which generalizes important geometric equations, like static vacuum and static perfect fluid. We investigate some geometric inequalities for those manifolds. Then, we…
The formation of bound states involving multiple particles underlies many interesting quantum physical phenomena, such as Efimov physics or superconductivity. In this work we show the existence of an infinite number of such states for some…
This article solves the initial boundary value problem for the vacuum Einstein equations with a negative cosmological constant in dimension 4, giving rise to asymptotically Anti-de Sitter spaces. We introduce a new family of geometric…
We introduce a new approach to constructing analytic solutions of the linear PDEs describing elastodynamics. This approach is illustrated for the case of a homogeneous isotropic half-plane body satisfying arbitrary initial conditions and…