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EnglishWe consider the weak solution of the Laplace equation in a planar domain with a straight crack, prescribing a homogeneous Neumann condition on the crack and a nonhomogeneous Dirichlet condition on the rest of the boundary. For every k we express the k-th derivative of the energy with respect to the crack length in terms of a finite number of coefficients of the asymptotic expansion of the solution near the crack tip and of a finite number of other parameters, which only depend on the shape of the domain. © 2014, Springer Basel.
Laplace equation in a domain with a rectilinear crack: higher order derivatives of the energy with respect to the crack length / Dal Maso, G.; Orlando, G.; Toader, R.. - In: NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS. - ISSN 1021-9722. - STAMPA. - 22:3(2015), pp. 449-476.
| Titolo: | Laplace equation in a domain with a rectilinear crack: higher order derivatives of the energy with respect to the crack length |
| Autori: | |
| Data di pubblicazione: | 2015 |
| Rivista: | |
| Citazione: | Laplace equation in a domain with a rectilinear crack: higher order derivatives of the energy with respect to the crack length / Dal Maso, G.; Orlando, G.; Toader, R.. - In: NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS. - ISSN 1021-9722. - STAMPA. - 22:3(2015), pp. 449-476. |
| Abstract: | We consider the weak solution of the Laplace equation in a planar domain with a straight crack, prescribing a homogeneous Neumann condition on the crack and a nonhomogeneous Dirichlet condition on the rest of the boundary. For every k we express the k-th derivative of the energy with respect to the crack length in terms of a finite number of coefficients of the asymptotic expansion of the solution near the crack tip and of a finite number of other parameters, which only depend on the shape of the domain. © 2014, Springer Basel. |
| Handle: | http://hdl.handle.net/11390/1095081 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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