Related papers: Optimal boundary gradient estimates for Lam\'{e} s…
We obtain an upper bound on the initial blow-up of nonnegative solutions of second order semilinear parabolic inequalities when a superlinear exponent in the inequalities is not too large.
We establish new, optimal gradient continuity estimates for solutions to a class of 2nd order partial differential equations, $\mathscr{L}(X, \nabla u, D^2 u) = f$, whose diffusion properties (ellipticity) degenerate along the \textit{a…
This paper presents a rigorous mathematical analysis of transverse electromagnetic (EM) field concentration between two adjacent obstacles within the framework of the quasi-static approximation. We investigate three degenerate conductivity…
We develop an optimal regularity theory for $L^p$-viscosity solutions of fully nonlinear uniformly elliptic equations in nondivergence form whose gradient growth is described through a Hamiltonian function with measurable and possibly…
In this paper, we establish the pointwise upper and lower bounds of the gradients of solutions to a class of elliptic systems, including linear systems of elasticity, in a general narrow region and in all dimensions. This problem arises…
The paper deals with blow--up for the solutions of wave equation with nonlinear source and nonlinear boudary damping terms, posed in a bounded and regular domain. The initial data are posed in the energy space. The aim of the paper is to…
Convergence of the solutions of nonhomogeneous linear singularly perturbed systems to that of the corresponding reduced singular system on the half-line [0, $\infty $) is considered. To include the situation on a neighborhood of initial…
We obtain an explicit upper bound on the size of the coefficients of the elliptic modular polynomials $\Phi_N$ for any $N\geq1$. These polynomials vanish at pairs of $j$-invariants of elliptic curves linked by cyclic isogenies of degree…
We study large deviations for some non-local parabolic type equations. We show that, under some assumptions on the non-local term, problems defined in a bounded domain converge with an exponential rate to the solution of the problem defined…
We study boundary blow-up solutions of semilinear elliptic equations $Lu=u_+^p$ with $p>1$, or $Lu=e^{au}$ with $a>0$, where $L$ is a second order elliptic operator with measurable coefficients. Several uniqueness theorems and an existence…
In this article, we provide upper and lower bounds for the growth rate of irreducible meanders. The obtained upper bound implies that the proportion of irreducible meanders among all of the prime meanders of order $n$ approaches $0$ as $n$…
This paper deals with the blow-up properties of positive solutions to a system of two heat equations.
We prove quantitative decay estimates for the boundary layer corrector in stochastic homogenization in the case of a half-space boundary. Our estimates are of optimal order and show that the gradient of the boundary layer corrector features…
This paper presents adaptive boundary element methods for positive, negative, as well as zero order operator equations, together with proofs that they converge at certain rates. The convergence rates are quasi-optimal in a certain sense…
We provide quantitative gradient bounds for solutions to certain parabolic equations with unbalanced polynomial growth and non-smooth coefficients.
Mathematical modeling of many physical processes such as diffusion, viscosity of fluids and combustion involves differential equations with small coefficients of higher derivatives. These may be small diffusion coefficients for modeling the…
We consider stochastic partial differential equations under minimal assumptions: the coefficients are merely bounded and measurable and satisfy the stochastic parabolicity condition. In particular, the diffusion term is allowed to be…
Performance of optimization on quadratic problems sensitively depends on the low-lying part of the spectrum. For large (effectively infinite-dimensional) problems, this part of the spectrum can often be naturally represented or approximated…
We consider a nonlinear heat equation with a gradient term. We construct a blow-up solution for this equation with a prescribed blow-up profile. For that, we translate the question in selfsimilar variables and reduce the problem to a finite…
This paper focuses on developing a conditional gradient algorithm for multiobjective optimization problems with an unbounded feasible region. We employ the concept of recession cone to establish the well-defined nature of the algorithm. The…