The main goal of this project is to study partial regularity of stationary and stable solutions to the Gelfand-Liouville equation. Due to the presence of the exponential nonlinearity, the natural scale invariant energy is not monotone increasing. To overcome this difficulty we propose to study these problems by analyzing the behavior of solutions around singular points, and a blow-up arguments. This involves compactness properties for a family of solutions and understanding homogeneous solutions on the whole Euclidean space.
Patents
0
Source
Source
Science and Engineering Research Board (SERB), DST 2022-23
Science and Engineering Research Board (SERB), New Delhi
Anusandhan National Research Foundation (ANRF)
Quick Information
Area of Research
Mathematical Sciences
Start Year
2023
End Year
2025
Sanction Amount
₹ 14.93 L
Status
Completed
Contact
hyder@tifrbng.res.in
Output
No. of Research Paper
00
Technologies (If Any)
00
No. of PhD Produced
00
No. of Patents
Filed :00
Grant :00
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