The weak maximum principle for degenerate elliptic equations: unbounded domains and systems

Italo Capuzzo Dolcetta; Italo Capuzzo Dolcetta

doi:10.3934/mine.2020036

Mathematics in Engineering

2020, Volume 2, Issue 4: 772-786. doi: 10.3934/mine.2020036

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The weak maximum principle for degenerate elliptic equations: unbounded domains and systems

Italo Capuzzo Dolcetta ^,

GNAMPA-INDAM, Roma, Italy

Received: 18 March 2020 Accepted: 06 July 2020 Published: 10 July 2020

This paper reviews a number of more or less recent results concerning the validity of Alexandrov-Bakelman-Pucci type estimates and the weak Maximum Principle for non smooth functions satisfying in the viscosity sense fully non linear elliptic partial differential inequalities in unbounded domains. The last section announces a very recent new result about the validity of the weak Maximum Principle for a class of degenerate elliptic cooperative systems.
- fully nonlinear elliptic differential equations,
- viscosity solutions,
- Alexandrov-Bakelman-Pucci estimates,
- maximum principle,
- cooperative systems
Citation: Italo Capuzzo Dolcetta. The weak maximum principle for degenerate elliptic equations: unbounded domains and systems[J]. Mathematics in Engineering, 2020, 2(4): 772-786. doi: 10.3934/mine.2020036

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Abstract

This paper reviews a number of more or less recent results concerning the validity of Alexandrov-Bakelman-Pucci type estimates and the weak Maximum Principle for non smooth functions satisfying in the viscosity sense fully non linear elliptic partial differential inequalities in unbounded domains. The last section announces a very recent new result about the validity of the weak Maximum Principle for a class of degenerate elliptic cooperative systems.

References

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