相关论文: On the Poisson Equation on a Surface with a bounda…

We present some new regularity criteria for suitable weak solutions of magnetohydrodynamic equations near boundary in dimension three. We prove that suitable weak solutions are H\"older continuous near boundary provided that either the…

This work deals with the Landau equation in a bounded domain with the Maxwell reflection condition on the boundary for any (possibly smoothly position dependent) accommodation coefficient and for the full range of interaction potentials,…

We consider a strongly nonlinear differential equation of the following general type $$(\Phi(a(t,x(t)) \, x'(t)))'= f(t,x(t),x'(t)), \quad \text{a.e. on $[0,T]$}$$ where $f$ is a Carath\'edory function, $\Phi$ is a strictly increasing…

In this paper, we investigate a sixth order elliptic equation with the simply supported boundary conditions in a polygonal domain. We propose a new method that decouples the sixth order problem into a system of second order equations.…

In this paper, it is proved that the weak convergence of the $L_p$ Guassian surface area measures implies the convergence of the corresponding convex bodies in the Hausdorff metric for $p\geq 1$. Moreover, this paper obtains the solution to…

In this paper we study on smooth bounded domains the global regularity (up to the boundary) for weak solutions to systems having $p$-structure depending only on the symmetric part of the gradient.

We show that finite-energy weak solutions to the incompressible Navier--Stokes equations on a three-dimensional bounded smooth domain are regular up to the boundary, provided that the $L^4_tL^4_x$-norm of the solution is smaller than a…

We consider the approximation of Poisson type problems where the source is given by a singular measure and the domain is a convex polygonal or polyhedral domain. First, we prove the well-posedness of the Poisson problem when the source…

We show an existence of a weak solution of a degenerate and/or singular semilinear elliptic boundary value (nonhomogeneous) problem lying between a given weak subsolution and a given weak supersolution. It has been applied for an existence…

In this paper we apply the newly born choice theory of the shape parameters contained in the smooth radial basis functions to solve Poisson equations. Some people complain that Luh's choice theory, based on harmonic analysis, is…

We consider the stochastic continuity equation associated to an It\^{o} diffusion with irregular drift and diffusion coefficients. We give regularity conditions under which weak solutions are renormalized in the sense of DiPerna/Lions, and…

We give a simple proof of the strong maximum principle for viscosity subsolutions of fully nonlinear elliptic PDEs on the form $$ F(x,u,Du,D^2u) = 0 $$ under suitable structure conditions on the equation allowing for non-Lipschitz growth in…

A three-dimensional (3D) Poisson solver with longitudinal periodic and transverse open boundary conditions can have important applications in beam physics of particle accelerators. In this paper, we present a fast efficient method to solve…

First, a new sufficient condition for uniqueness of weak solutions is proved for the system of 2D viscous Primitive Equations. Second, global existence and uniqueness are established for several classes of weak solutions with partial…

We are concerned with the nonexistence of sign-changing global weak solutions for a class of semilinear parabolic differential inequalities with convection terms in exterior domains. A weight function of the form $t^\alpha |x|^\sigma$ is…

We establish the equivalence between weak and viscosity solutions for non-homogeneous $p(x)$-Laplace equations with a right-hand side term depending on the spatial variable, the unknown, and its gradient. We employ inf- and sup-convolution…

We treat the exterior Dirichlet problem for a class of fully nonlinear elliptic equations of the form $$f(\lambda(D^2u))=g(x),$$ with prescribed asymptotic behavior at infinity. The equations of this type had been studied extensively by…

We consider Dirichlet problems for linear elliptic equations of second order in divergence form on a bounded or exterior smooth domain $\Omega$ in $\mathbb{R}^n$, $n \ge 3$, with drifts $\mathbf{b}$ in the critical weak $L^n$-space…

We present an efficient numerical method, inspired by transformation optics, for solving the Poisson equation in complex and arbitrarily shaped geometries. The approach operates by mapping the physical domain to a uniform computational…

We present a nonvariational setting for the Neumann problem for the Poisson equation for solutions that are H\"{o}lder continuous and that may have infinite Dirichlet integral. We introduce a distributional normal derivative on the boundary…