On the Dirichlet Problem with Corner Singularity
نویسندگان
چکیده
منابع مشابه
On a Method to Subtract off a Singularity at a Corner for the Dirichlet or Neumann Problem
Let D be a plane domain partly bounded by two line segments which meet at the origin and form there an interior angle va > 0. Let U(x, y) be a solution in D of Poisson's equation such that either U or dll/dn (the normal derivative) takes prescribed values on the boundary segments. Let U(x, y) be sufficiently smooth away from the corner and bounded at the corner. Then for each positive integer N...
متن کاملThe stability of the solution of an inverse spectral problem with a singularity
This paper deals with the singular Sturm-Liouville expressions $ ell y = -y''+q(x)y=lambda y $ on a finite interval, where the potential function $q$ is real and has a singularity inside the interval. Using the asymptotic estimates of a spectral fundamental system of solutions of Sturm-Liouville equation, the asymptotic form of the solution of the equation (0.1) and the ...
متن کاملDirichlet Duality and the Nonlinear Dirichlet Problem on Riemannian Manifolds
In this paper we study the Dirichlet problem for fully nonlinear secondorder equations on a riemannian manifold. As in our previous paper [HL4] we define equations via closed subsets of the 2-jet bundle where each equation has a natural dual equation. Basic existence and uniqueness theorems are established in a wide variety of settings. However, the emphasis is on starting with a constant coeff...
متن کاملOn Approximating the Corner Cover Problem
The rectilinear polygon cover problem is one in which a certain class of features of a rectilinear polygon of n vertices has to be covered with the minimum number of rectangles included in the polygon. In particular, one can consider covering the entire interior, the boundary and the set of corners of the polygon. These problems have important applications in, for example, storing images and in...
متن کاملThe Dirichlet Problem on the Hyperbolic Ball
(1.2) PIH : C(Sn−1) −→ C(B) ∩ C∞(Bn), such that u = PIH f solves (1.2A) ∆Hu = 0 on B, u ∣∣ Sn−1 = f. Here, ∆H is the Laplace-Beltrami operator on B, with metric tensor (1.1). We will establish further regularity on u = PIH f when f has some further smoothness on Sn−1, and estimate du(x), in the hyperbolic metric, as x → ∂B. If n = 2, then ∆Hu = 0 if and only if ∆u = 0, where ∆ = ∂ 1 +∂ 2 2 is t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics
سال: 2020
ISSN: 2227-7390
DOI: 10.3390/math8111870