We investigate the positive solutions of the semilinear parabolic system with coupled nonlinear nonlocal sources subject to weighted nonlocal Dirichlet boundary conditions. The blow-up and global existence criteria are obtained.

We study two types of asymptotic problems whose common feature and difficultyis to exhibit oscillating Dirichlet boundary conditions : the main contribution of this article is to show how to recover the Dirichlet boundary condition for the limiting equation. These two types of problems are (i) periodic homogenization problems for fully nonlinear, second-order elliptic partial differential equat...

A classical result of Dirichlet shows that certain elementary character sums compute class numbers of quadratic imaginary number fields. We obtain analogous relations between class numbers and a weighted character sum associated to a 2-isogeny of elliptic curves.

In this article, we prove some weighted pointwise estimates for three discontinuous Galerkin methods with lifting operators appearing in their corresponding bilinear forms. We consider a Dirichlet problem with a general second order elliptic operator.

In this work, we show the convergence of adaptive lowest-order FEM (AFEM) for an elliptic obstacle problem with non-homogeneous Dirichlet data, where the obstacle χ is restricted only by χ ∈ H2(Ω). The adaptive loop is steered by some residual based error estimator introduced in Braess, Carstensen & Hoppe (2007) that is extended to control oscillations of the Dirichlet data, as well. In the spi...

We obtain a noncommutative multivariable analogue of Louhichi and Olofsson characterization Toeplitz operators with harmonic symbols on the weighted Bergman space $A_m({\bf D})$, as well Eschmeier Langendorfer extension to unit ball ${\bf C}^n$. All our results are proved in more general setting poly-hyperballs D_n^m}(H)$, n,m}\in {\bf N}^k$, used characterize bounded free $k$-pluriharmonic fun...

Abstract In this paper, we study a nonlocal approximation of the time-dependent (local) Eikonal equation with Dirichlet-type boundary conditions, where kernel in problem is properly scaled. Based on theory viscosity solutions, prove existence and uniqueness solutions both local problems, as well regularity properties these time space. We then derive error bounds between solution to that one, co...

We consider the aff(1)-module structure on the spaces of bilinear differential operators acting on the spaces of weighted densities. We compute the first differential cohomology of the Lie superalgebra aff(1) with coefficients in space Dλ,ν;µ of bilinear differential operators acting on weighted densities. We study also the super analogue of this problem getting the same results.