Explicit Estimates for Solutions of Mixed Elliptic Problems
Author
Source
International Journal of Partial Differential Equations
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-16, 16 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-03-31
Country of Publication
Egypt
No. of Pages
16
Main Subjects
Abstract EN
We deal with the existence of quantitative estimates for solutions of mixed problems to an elliptic second-order equation in divergence form with discontinuous coefficients.
Our concern is to estimate the solutions with explicit constants, for domains in ℝn (n≥2) of class C0,1.
The existence of L∞ and W1,q estimates is assured for q=2 and any q The proof method of the quantitative L∞ estimates is based on the De Giorgi technique developed by Stampacchia. By using the potential theory, we derive W1,p estimates for different ranges of the exponent p depending on the fact that the coefficient is either Dini-continuous or only measurable and bounded. In this process, we establish new existences of Green functions on such domains. The last but not least concern is to unify (whenever possible) the proofs of the estimates to the extreme Dirichlet and Neumann cases of the mixed problem.
American Psychological Association (APA)
Consiglieri, Luisa. 2014. Explicit Estimates for Solutions of Mixed Elliptic Problems. International Journal of Partial Differential Equations،Vol. 2014, no. 2014, pp.1-16.
https://search.emarefa.net/detail/BIM-502825
Modern Language Association (MLA)
Consiglieri, Luisa. Explicit Estimates for Solutions of Mixed Elliptic Problems. International Journal of Partial Differential Equations No. 2014 (2014), pp.1-16.
https://search.emarefa.net/detail/BIM-502825
American Medical Association (AMA)
Consiglieri, Luisa. Explicit Estimates for Solutions of Mixed Elliptic Problems. International Journal of Partial Differential Equations. 2014. Vol. 2014, no. 2014, pp.1-16.
https://search.emarefa.net/detail/BIM-502825
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-502825