Author | Neuberger, John William. author |
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Title | Sobolev Gradients and Differential Equations [electronic resource] / by John William Neuberger |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1997 |
Connect to | http://dx.doi.org/10.1007/BFb0092831 |
Descript | VIII, 152 p. online resource |
Several gradients -- Comparison of two gradients -- Continuous steepest descent in Hilbert space: Linear case -- Continuous steepest descent in Hilbert space: Nonlinear case -- Orthogonal projections, Adjoints and Laplacians -- Introducing boundary conditions -- Newton's method in the context of Sobolev gradients -- Finite difference setting: the inner product case -- Sobolev gradients for weak solutions: Function space case -- Sobolev gradients in non-inner product spaces: Introduction -- The superconductivity equations of Ginzburg-Landau -- Minimal surfaces -- Flow problems and non-inner product Sobolev spaces -- Foliations as a guide to boundary conditions -- Some related iterative methods for differential equations -- A related analytic iteration method -- Steepest descent for conservation equations -- A sample computer code with notes