The Numerical Solution Of Elliptic Partial Differential Equations By The Method Of Lines.
The numerical solution of large finite element systems by explicit preconditioning semi-direct methods
The Numerical Solution of the Inverse Stefan Problem.
The Oblique Derivative Problem. I.
The obstacle problem for the -harmonic equation.
The obstacle problem for the biharmonic operator
The operator for the wave equation with Dirichlet control.
The optimal control problem in coefficients for the pseudoparabolic variational inequality
The optimal shape of a dendrite sealed at both ends
The optimization of eigenvalue problems involving the -Laplacian.
The optimization of the stationary heat equation with a variable right-hand side
Solving the stationary heat equation we optimize the temperature on part of the boundary of the domain under investigation. First the Poisson equation is solved; both the Neumann condition on part of the boundary and the Newton condition on the rest are prescribed, the distribution of the heat sources being variable. In the second case, the heat equation also contains a convective term, the distribution of heat sources is specified and the Neumann condition is variable on part of the boundary.
The Ordering of Tridiagonal Matrices in the Cyclic Reduction Method for Poisson's Equation.
The oscillatory behavior of second order nonlinear elliptic equations.
The output least squares identifiability of the diffusion coefficient from an H–observation in a 2–D elliptic equation
Output least squares stability for the diffusion coefficient in an elliptic equation in dimension two is analyzed. This guarantees Lipschitz stability of the solution of the least squares formulation with respect to perturbations in the data independently of their attainability. The analysis shows the influence of the flow direction on the parameter to be estimated. A scale analysis for multi-scale resolution of the unknown parameter is provided.
The Output Least Squares Identifiability of the Diffusion Coefficient from an H1–Observation in a 2–D Elliptic Equation
Output least squares stability for the diffusion coefficient in an elliptic equation in dimension two is analyzed. This guarantees Lipschitz stability of the solution of the least squares formulation with respect to perturbations in the data independently of their attainability. The analysis shows the influence of the flow direction on the parameter to be estimated. A scale analysis for multi-scale resolution of the unknown parameter is provided.
The overdetermined Cauchy problem
We consider the (characteristic and non-characteristic) Cauchy problem for a system of constant coefficients partial differential equations with initial data on an affine subspace of arbitrary codimension. We show that evolution is equivalent to the validity of a principle on the complex characteristic variety and we study the relationship of this condition with the one introduced by Hörmander in the case of scalar operators and initial data on a hypersurface.
The -Laplace eigenvalue problem as in a Finsler metric
We consider the -Laplacian operator on a domain equipped with a Finsler metric. We recall relevant properties of its first eigenfunction for finite and investigate the limit problem as .
The -Laplacian and connected pairs of functions.
The -Laplacian in domains with small random holes
{ll -div (|Duh|p-2 Duh)=g, & in D Eh uhH1,p0(D Eh). . where and are random subsets of a bounded open set of . By...
The -Laplacian – mascot of nonlinear analysis.