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User’s guide to viscosity solutions of second order partial differential equations
Open accessAbstract
The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorems, and theorems about continuous dependence may now be proved by very efficient and striking arguments. The range of important applications of these results is enormous. This article is a self-contained exposition of the basic theory of viscosity solutions.
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Cited by
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A Unified Framework for Hybrid Control: Model and Optimal Control Theory
Branicky, M. S., Borkar, V. S., & Mitter, S. K. (1998) · IEEE Transactions on Automatic Control · doi:10.1109/9.654885 · Cited by 1,313
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Metadata
- Authors
- Crandall, M. G., Ishii, H., & Lions, P.-L.
- Venue
- Bulletin of the American Mathematical Society
- Publisher
- American Mathematical Society (AMS)
- Published
- 1992
- Volume
- 27
- Issue
- 1
- Pages
- 1-67
- ISSN
- 0002-9904 (ISSN-L)
- 0273-0979
- 1088-9485
- OpenAlex
- W2032316144
- Cited by
- 4,781
- References
- 0
- FWCI
- 69.34
- Type
- journal article
- Language
- en
- Open access
- diamond
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- CoChat. (2026). Citation check: User’s guide to viscosity solutions of second order partial differential equations. https://app.cochat.ai/papers/10.1090/s0273-0979-1992-00266-5
- The paper
- Crandall, M. G., Ishii, H., & Lions, P.-L. (1992). User’s guide to viscosity solutions of second order partial differential equations. Bulletin of the American Mathematical Society. https://doi.org/10.1090/s0273-0979-1992-00266-5
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
