Laplace operator, variable exponent Sobolev spaces, second derivatives MSC (2010) 35Bxx, 35Jxx In this paper, we establish second order regularity for the p(x)-Laplace operator. This generalizes classical results known when the function p(.) is equal to some constant p > 1.
Regularity of the obstacle problem for a fractional power of the laplace operator
โ Scribed by Luis Silvestre
- Publisher
- John Wiley and Sons
- Year
- 2006
- Tongue
- English
- Weight
- 332 KB
- Volume
- 60
- Category
- Article
- ISSN
- 0010-3640
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
An optimal control problem of the obstacle for an elliptic variational inequality is considered, in which the obstacle is regarded as the control. To get the regularity of the optimal pair, a new related control problem is introduced. By proving the existence of an optimal pair to such a new control
For the Tricomi equation with Dirichlet boundary conditions, we study the relationship between singularites at the boundary and singularities in the interior of a bounded planar region with smooth non-characteristic boundary. Necessary and sufficient conditions for interior smoothness are stated in
## A posteriori error estimation of the p-Laplace problem Two a posteriori error estimates are discussed for the p-Laplace problem. Up to errors in their numerical computation, they provide a guaranteed upper bound for the W 1,p -seminorm and a weighted W 1,2 -seminorm of uu h . The first, sharper
We describe regularity results for viscosity solutions of a fully nonlinear (possible degenerate) second-order elliptic PDE with inhomogeneous Neumann boundary condition holding in the generalized sense. These results only require that 0 is uniformly convex, 0 # C 1, / for some / # (0, 1) and that t