On Neumann problem for the degenerate Monge–Ampère type equations
Abstract In this paper, we study the global C 1 , 1 $C^{1, 1}$ regularity for viscosity solution of the degenerate Monge–Ampère type equation det [ D 2 u − A ( x , D u ) ] = B ( x , u , D u ) $\det [D^{2}u-A(x, Du)]=B(x, u, Du)$ with the Neumann boundary value condition D ν u = φ ( x ) $D_{\nu }u=\v...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2021-01-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13661-021-01486-w |
| Summary: | Abstract In this paper, we study the global C 1 , 1 $C^{1, 1}$ regularity for viscosity solution of the degenerate Monge–Ampère type equation det [ D 2 u − A ( x , D u ) ] = B ( x , u , D u ) $\det [D^{2}u-A(x, Du)]=B(x, u, Du)$ with the Neumann boundary value condition D ν u = φ ( x ) $D_{\nu }u=\varphi (x)$ , where the matrix A is under the regular condition and some structure conditions, and the right-hand term B is nonnegative. |
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| ISSN: | 1687-2770 |