Sign-preserving property for some fourth-order elliptic operators in one dimension or in radial symmetry
نویسندگان
چکیده
منابع مشابه
Sign-preserving Property for Some Fourth-order Elliptic Operators in One Dimension and Radial Symmetry
For a class of one-dimensional linear elliptic fourth-order equations with homogeneous Dirichlet boundary conditions it is shown that a non-positive and non-vanishing right-hand side gives rise to a negative solution. A similar result is obtained for the same class of equations for radially symmetric solutions in a ball or in an annulus. Several applications are given, including applications to...
متن کاملDegenerate elliptic operators in one dimension
Let H be the symmetric second-order differential operator on L2(R) with domain C c (R) and action Hφ = −(c φ ) where c ∈ W 1,2 loc (R) is a real function which is strictly positive on R\{0} but with c(0) = 0. We give a complete characterization of the self-adjoint extensions and the submarkovian extensions of H . In particular if ν = ν+ ∨ ν− where ν±(x) = ± ∫ ±1 ±x c then H has a unique self-ad...
متن کاملResolvent Estimates for Elliptic Finite Element Operators in One Dimension
We prove the analyticity (uniform in h ) of the semigroups generated on Lp(0, 1), 1 < p < oo , by finite element analogues Ah of a onedimensional second-order elliptic operator A under Dirichlet boundary conditions. This is accomplished by showing the appropriate estimates for the resolvents by means of energy arguments. The results are applied to prove stability and optimal-order error bounds ...
متن کاملOrder parameter for symmetry-protected phases in one dimension.
We introduce an order parameter for symmetry-protected phases in one dimension which allows us to directly identify those phases. The order parameter consists of stringlike operators and swaps, but differs from conventional string order operators in that it only depends on the symmetry but not on the state. We verify our framework through numerical simulations for the SO(3) invariant spin-1 bil...
متن کاملTwo weak solutions for some singular fourth order elliptic problems
In this paper, we establish the existence of at least two distinct weak solutions for some singular elliptic problems involving a p-biharmonic operator, subject to Navier boundary conditions in a smooth bounded domain in RN . A critical point result for differentiable functionals is exploited, in order to prove that the problem admits at least two distinct nontrivial weak solutions.
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: Journal d'Analyse Mathématique
سال: 2015
ISSN: 0021-7670,1565-8538
DOI: 10.1007/s11854-015-0024-2