共查询到20条相似文献,搜索用时 0 毫秒
1.
2.
3.
A. Lunardi G. Metafune D. Pallara 《Proceedings of the American Mathematical Society》2005,133(9):2625-2635
We study the realisation of the operator in with Dirichlet boundary condition, where is a possibly unbounded open set in , is a semi-convex function and the measure lets be formally self-adjoint. The main result is that at is a dissipative self-adjoint operator in .
4.
5.
Murray Cantor 《Journal of Differential Equations》1979,34(1):102-113
In this paper we show the Dirichlet and Neumann problems over exterior regions have unique solutions in certain weighted Sobolev spaces. Two applications are given: (1) The Dirichlet problem for semi-linear operators, and (2) a Helmholtz decomposition for vector fields on exterior regions. 相似文献
6.
In this paper, we present examples of nondivergence form of second-order elliptic operators with continuous coefficients, such that L has an irregular boundary point that is regular for the Laplacian. Also for any eigenvalue spread <1 of the matrix of the coefficients, we provide an example of operator with discontinuous coefficients that has regular boundary points nonequivalent to Laplacian’s (we give examples for each direction of nonequivalence). All examples are constructed for each dimension starting with 3. 相似文献
7.
8.
9.
10.
11.
12.
13.
In this paper we complete the study of the regularity of the free boundary in two-phase problems for linear elliptic operators started in [M.C. Cerutti, F. Ferrari, S. Salsa, Two-phase problems for linear elliptic operators with variable coefficients: Lipschitz free boundaries are C1,γ, Arch. Ration. Mech. Anal. 171 (2004) 329-348]. In particular we prove that Lipschitz and flat free boundaries (in a suitable sense) are smooth. As byproduct, we prove that Lipschitz free boundaries are smooth in the case of quasilinear operators of the form div(A(x,u)∇u) with Lipschitz coefficients. 相似文献
14.
15.
16.
17.
We investigate manifolds with boundary in noncommutative geometry. Spectral triples associated to a symmetric differential operator and a local boundary condition are constructed. We show that there is no tadpole for classical Dirac operators with a chiral boundary condition on spin manifolds. 相似文献
18.
19.
Sven Beuchler Clemens Pechstein Daniel Wachsmuth 《Computational Optimization and Applications》2012,51(2):883-908
We investigate the discretization of optimal boundary control problems for elliptic equations on two-dimensional polygonal
domains by the boundary concentrated finite element method. We prove that the discretization error ||u*-uh*||L2(G)\|u^{*}-u_{h}^{*}\|_{L^{2}(\Gamma)} decreases like N
−1, where N is the total number of unknowns. This makes the proposed method favorable in comparison to the h-version of the finite element method, where the discretization error behaves like N
−3/4 for uniform meshes. Moreover, we present an algorithm that solves the discretized problem in almost optimal complexity. The
paper is complemented with numerical results. 相似文献
20.