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Item Details
| Title:
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POLYHARMONIC BOUNDARY VALUE PROBLEMS
POSITIVITY PRESERVING AND NONLINEAR HIGHER ORDER ELLIPTIC EQUATIONS IN BOUNDED DOMAINS |
| By: |
Filippo Gazzola, Hans-Christoph Grunau, Bernd Kawohl |
| Format: |
Paperback |
| List price:
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£62.99 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
3642122442 |
| ISBN 13: |
9783642122446 |
| Publisher: |
SPRINGER-VERLAG BERLIN AND HEIDELBERG GMBH & CO. KG |
| Pub. date: |
3 June, 2010 |
| Edition: |
2010 ed. |
| Series: |
Lecture Notes in Mathematics v. 1991 |
| Pages: |
423 |
| Description: |
This accessible monograph covers higher order linear and nonlinear elliptic boundary value problems in bounded domains, mainly with the biharmonic or poly-harmonic operator as leading principal part. It provides rapid access to recent results and references. |
| Synopsis: |
Linear elliptic equations arise in several models describing various phenomena in the applied sciences, the most famous being the second order stationary heat eq- tion or,equivalently,the membraneequation. Forthis intensivelywell-studiedlinear problem there are two main lines of results. The ?rst line consists of existence and regularity results. Usually the solution exists and "gains two orders of differen- ation" with respect to the source term. The second line contains comparison type results, namely the property that a positive source term implies that the solution is positive under suitable side constraints such as homogeneous Dirichlet bou- ary conditions. This property is often also called positivity preserving or, simply, maximum principle. These kinds of results hold for general second order elliptic problems, see the books by Gilbarg-Trudinger [198] and Protter-Weinberger [347]. For linear higher order elliptic problems the existence and regularitytype results - main, as one may say, in their full generality whereas comparison type results may fail. Here and in the sequel "higher order" means order at least four. Most interesting models, however, are nonlinear.By now, the theory of second order elliptic problems is quite well developed for semilinear, quasilinear and even for some fully nonlinear problems. If one looks closely at the tools being used in the proofs, then one ?nds that many results bene?t in some way from the positivity preserving property. Techniques based on Harnack's inequality, De Giorgi-Nash- Moser's iteration, viscosity solutions etc. |
| Illustrations: |
18 black & white illustrations, biography |
| Publication: |
Germany |
| Imprint: |
Springer-Verlag Berlin and Heidelberg GmbH & Co. K |
| Returns: |
Returnable |
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