Related papers: Continuation of global solution curves using globa…
In this paper, we generalize the $W^{2,p}$ interior estimates of fully nonlinear elliptic equations that were obtained by Caffarelli in [1]. The generalizations are carried out in two directions. One is that we relax the regularity…
The ancient unsolved problem of congruent numbers has been reduced to one of the major questions of contemporary arithmetic: the finiteness of the number of curves over $\bf Q$ which become isomorphic at every place to a given curve. We…
A numerical scheme is presented for solving the Helmholtz equation with Dirichlet or Neumann boundary conditions on piecewise smooth open curves, where the curves may have corners and multiple junctions. Existing integral equation methods…
We investigate global and local regularity of generalized solutions to parabolic initial-boundary value problem for Petrovskii system of second order differential equations. Results are formulated in terms of the belonging of right-hand…
We consider an evolving plane curve with two endpoints that can move freely on the $x$-axis with generating constant contact angles. We discuss the asymptotic behavior of global-in-time solutions when the evolution of this plane curve is…
In this article we study $p$-biharmonic curves as a natural generalization of biharmonic curves. In contrast to biharmonic curves $p$-biharmonic curves do not need to have constant geodesic curvature if $p=\frac{1}{2}$ in which case their…
Let $p$ be a prime. We discuss methods of solution of congruences modulo $p^n$ using $p$-adic numbers; these methods are similar to computations with real numbers (local methods). Examples of relations between local and global methods are…
We consider a time-fractional parabolic equation of doubly nonlinear type, featuring nonlinear terms both inside and outside the differential operator in time. The main nonlinearities are maximal monotone graphs, without restrictions on the…
We prove that circle graphs (intersection graphs of circle chords) can be embedded as intersection graphs of rays in the plane with polynomial-size bit complexity. We use this embedding to show that the global curve simplification problem…
We construct the global bifurcation curves, solutions versus level of harvesting, for the steady states of a diffusive logistic equation on a bounded domain, under Dirichlet boundary conditions and other appropriate hypotheses, when $a$,…
We establish the global gradient bounds for weak solutions to the elliptic variational inequality with two-sided obstructions, associated with a $p(x)$-Laplacian type operator involving degenerate or singular matrix weights. Under the…
We study the problem of approximation of 2D set of points. Such type of problems always occur in physical experiments, econometrics, data analysis and other areas. The often problems of outliers or spikes usually make researchers to apply…
We consider the bifurcation diagram of radial solutions for the Gelfand problem with a positive radially symmetric weight in the unit ball. We deal with the exponential nonlinearity and a power-type nonlinearity. When the weight is…
We consider the Gelfand problem with general supercritical nonlinearities in the two-dimensional unit ball. In this paper, we prove the non-existence of an unstable solution for any positive small parameter $\lambda$. The result implies…
In this paper we prove global bounds on the spatial gradient of viscosity solutions to second order linear and nonlinear parabolic equations in $(0,T) \times \R^N$. Our assumptions include the case that the coefficients be both unbounded…
In this paper we construct parameterizations of elliptic curves over the rationals which have many consecutive integral multiples. Using these parameterizations, we perform searches in GMP and Magma to find curves with points of small…
Existence of global regular solution branches of the Boltzmann Cauchy problem with continuously differentiable data in phase space dimension $2d\geq 6$ with polynomial decay at infinity of order greater than $2d$ is proved. There are data…
We classify global Lipschitz solutions to two-phase free boundary problems governed by concave fully nonlinear equations, as either two-plane solutions or solutions to a one-phase problem.
In this paper we extend existing results concerning generalized eigenvalues of Pucci's extremal operators. In the radial case, we also give a complete description of their spectrum, together with an equivalent of Rabinowitz's Global…
A new method is introduced for solving Laplace problems on 2D regions with corners by approximation of boundary data by the real part of a rational function with fixed poles exponentially clustered near each corner. Greatly extending a…