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Contribution Details
| Type | Journal Article |
| Scope | Discipline-based scholarship |
| Title | Eigenvalue distribution of some fractal semi-elliptic differential operators |
| Organization Unit | |
| Authors |
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| Item Subtype | Original Work |
| Refereed | Yes |
| Status | Published in final form |
| Language |
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| Journal Title | Mathematische Zeitschrift |
| Publisher | Springer |
| Geographical Reach | international |
| ISSN | 0025-5874 |
| Volume | 236 |
| Number | 2 |
| Page Range | 291 - 320 |
| Date | 2001 |
| Abstract Text | We consider differential operators of type Au(x) &=& u(x) + (-1)^{t_1}\frac{\partial ^{2t_1} u(x)}{\partial x_1^{2t_1}}+ (-1)^{t_2}\frac{\partial ^{2t_2} u(x)}{\partial x_2^{2t_2}} , x&=& (x_1,x_2)\in \R ^2 , and Sierpinski carpets \G⊂\R$^2$. The aim of the paper is to investigate spectral properties of the fractal differential operator A$^{−1}$∘tr$^Γ$ acting in the anisotropic Sobolev space W$^{(t1,t2)}$2(R$^2$) where tr$^Γ$ is closely related to the trace operator tr$_Γ$. |
| Free access at | DOI |
| Official URL | http://www.math.ethz.ch/~farkas/research/F.pdf |
| Digital Object Identifier | 10.1007/PL00004832 |
| Other Identification Number | merlin-id:4262 |
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