Related papers: Kazdan-Warner obstructions for a 4$th-$order bound…
We provide some obstructions to the prescribed Q-curvature problem for the complete conformal metrics on $\mathbb{R}^n$ with finite total Q-curvature. One of them is a Bonnet-Mayer type theorem with respect to Q-curvature. Others are…
In this paper we study the problem of prescribing the Gaussian curvature under a conformal change of the metric. We are concerned with the problem posed on a subdomain of the 2-sphere under Neumann boundary conditions of the conformal…
We study a class of boundary value problems with $\varphi$-Laplacian (e.g., the prescribed mean curvature equation, in which $\varphi(s)=\frac{s}{\sqrt{1+s^2}}$) \begin{center} $-\left(\varphi(u')\right)'=\lambda f(u)\; \text{ on }(-L,…
On a manifold with boundary, we deform the metric conformally. This induces a deformation of the Schouten tensor. We fix the metric at the boundary and realize a prescribed value for the product of the eigenvalues of the Schouten tensor in…
An initial-boundary value problem for the n-dimensional ($n$ is a natural number from the interval [2,7]) Kuramoto-Sivashinsky-Zakharov-Kuznetsov equation posed on smooth bounded domains in $\mathbb{R}^n$ was considered. The existence and…
The implications of restricted conformal invariance under conformal transformations preserving a plane boundary are discussed for general dimensions $d$. Calculations of the universal function of a conformal invariant $\xi$ which appears in…
We consider the problem of prescribing Gaussian and geodesic curvatures for a conformal metric on the unit disk. This is equivalent to solving the following P.D.E. \begin{equation*}\begin{cases}-\Delta u=2K(z)e^u&\hbox{in}\;\mathbb{D}^2,\\…
We here establish the higher fractional differentiability for solutions to a class of obstacle problems with non-standard growth conditions. We deal with the case in which the solutions to the obstacle problems satisfy a variational…
In this paper we theoretically show that interior-point methods based on self-concordant barriers possess favorable global complexity beyond their standard application area of convex optimization. To do that we propose first- and…
This work introduces topological regularization as a framework for handling ultraviolet divergences in quantum field theory, reinterpreting infinities as topological obstructions at spacetime boundaries. Through geometric compactification…
The main goal of this paper is the study of two kinds of nonlinear problems depending on parameters in unbounded domains. Using a nonstandard variational approach, we first prove the existence of bounded solutions for nonlinear eigenvalue…
This article deals with the variable coefficient thin obstacle problem in $n+1$ dimensions. We address the regular free boundary regularity, the behavior of the solution close to the free boundary and the optimal regularity of the solution…
We use the numerical conformal bootstrap to study boundary quantum electrodynamics, the theory of a four dimensional photon in a half space coupled to charged conformal matter on the boundary. This system is believed to be a boundary…
We consider a spacetime singularity at $t = 0$ arising in a Kasner-type metric that solves the gravitational equations modified by quantum effects of a conformal field theory (CFT). The resulting constraints can be solved efficiently when…
Recently, reduced order modeling methods have been applied to solving inverse boundary value problems arising in frequency domain scattering theory. A key step in projection-based reduced order model methods is the use of a sesquilinear…
This paper introduces a fast and numerically stable algorithm for the solution of fourth-order linear boundary value problems on an interval. This type of equation arises in a variety of settings in physics and signal processing. Our method…
Studies on Kazdan--Warner equations on graphs have grown steadily, yet the fractional case remains insufficiently explored. Using topological degree theory, this work investigates the fractional Kazdan--Warner equation in the negative case…
A fourth-order compact scheme is proposed for a fourth-order subdiffusion equation with the first Dirichlet boundary conditions. The fourth-order problem is firstly reduced into a couple of spatially second-order system and we use an…
Teichm\"uller's classical mapping problem for plane domains concerns finding a lower bound for the maximal dilatation of a quasiconformal homeomorphism which holds the boundary pointwise fixed, maps the domain onto itself, and maps a given…
We consider a variational problem with a polyconvex integrand and nonstandard boundary conditions that can be treated as minimization of the stress energy during the suturing process in the plastic surgery. Ex- istence of minimizers is…