Kaitan Antara Ruang Sobolev dan Ruang Lebesgue
DOI:
https://doi.org/10.14421/fourier.2017.61.21-26Keywords:
Lebesgue Space, Sobolev SpaceAbstract
Measureable function space and its norm with integral form has been known, one of which is Lebegsue Space and Sobolev Space. In applied Mathematics like in finding solution of partial differential equations, that two spaces is soo usefulness. Sobolev space is subset of Lebesgue space, its mean if we have a function that element of Sobolev Space then its element of Lebesgue space. But the converse of this condition is not applicable. In this research, we will give an example to shows that there is a function element of Lebesgue space but not element of Sobolev space
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References
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[2] Darmawijaya, S., 2006, Pengantar Analisis Real, Jurusan Matematika Fakultas MIPA Universitas Gadjah Mada, Yogyakarta.
[3] Darmawijaya, S., 2007, Pengantar Analisis Abstrak, Jurusan Matematika Fakultas MIPA Universitas Gadjah Mada, Yogyakarta.
[4] Debnath, L., and Mikusinski, P., 1999, Introduction to Hilbert Spaces with Applications, Second Edition, Academic Press, United States of America.
[5] Fife P.C., 1988, Dynamics of Intenal Layers and Diffusive Interfaces, CBMS-NSF Regional Conference Series in Applied Mathematics, SIAM, 53, Philadelphia.
[6] Friedman, A., 1982, Variational Principles and Free Boundary Problems, John Wiley & Sons, Inc., United States of America.
[7] Milan Miklavcic, 1998, Applied Functional Analysis and Partial Differential Equations, World Scientific Publishing Co.pte.Ltd., Singapore.
[8] Oden, J., T., and Reddy, J., N., 1976, An Introduction to the Mathematical Theory of Finite Elements, John Wiley & Sons, Inc., United States of America.
[9] Parzynski, W.R., and Zipse, P.W., 1982, Introduction to Mathematical Analysis, McGraw-Hill,United States of America.
[10] Schwartz, A., 1960, Analytic Geometry and Calculus, Holt, Rinehart and Winston, Inc., United States of America.
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Published
2017-04-03
How to Cite
Rahayu, P. P. (2017). Kaitan Antara Ruang Sobolev dan Ruang Lebesgue. Jurnal Fourier, 6(1), 21–26. https://doi.org/10.14421/fourier.2017.61.21-26
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