نتایج جستجو برای: biharmonic equation

تعداد نتایج: 230628  

2009
Hans-Christoph Grunau Frédéric Robert

In general, higher order elliptic equations and boundary value problems like the biharmonic equation or the linear clamped plate boundary value problem do not enjoy neither a maximum principle nor a comparison principle or – equivalently – a positivity preserving property. The problem is rather involved since the clamped boundary conditions prevent the boundary value problem from being written ...

2009
Joel Kilty Zhongwei Shen

We show that a bilinear estimate for biharmonic functions in a Lipschitz domain Ω is equivalent to the solvability of the Dirichlet problem for the biharmonic equation in Ω. As a result, we prove that for any given bounded Lipschitz domain Ω in Rd and 1 < q < ∞, the solvability of the Lq Dirichlet problem for ∆2u = 0 in Ω with boundary data in WA(∂Ω) is equivalent to that of the Lp regularity p...

Journal: :Computer Methods in Applied Mechanics and Engineering 2007

2006
Zhongwei Shen

Abstract. Let Ω be a bounded Lipschitz domain in R. We develop a new approach to the invertibility on L(∂Ω) of the layer potentials associated with elliptic equations and systems in Ω. As a consequence, for n ≥ 4 and 2(n−1) n+1 − ε < p < 2 where ε > 0 depends on Ω, we obtain the solvability of the L Neumann type boundary value problems for second order elliptic systems. The analogous results fo...

Journal: :J. Computational Applied Mathematics 2010
Peter Junghanns Giovanni Monegato A. Strozzi

We consider integral equation formulations of contact problems of Kirchhoff (thin) plates, discontinuously supported along arcs or segments. In the classical PDE formulation (biharmonic equation), the plate deflection is assumed as the primary unknown. The boundary conditions along the supported edge are imposed in terms of the plate deflection and its derivatives, and the reaction forces and c...

2015
ZONGMING GUO JUNCHENG WEI FENG ZHOU

Positive singular radial entire solutions of a biharmonic equation with subcritical exponent are obtained via the entire radial solutions of the equation with supercritical exponent and the Kelvin transformation. The expansions of such singular radial solutions at the singular point 0 are presented. Using these singular radial entire solutions, we construct solutions with a prescribed singular ...

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