Regularity for Hamilton-Jacobi equations via approximation
1995 ◽
Vol 51
(2)
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pp. 195-213
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Keyword(s):
We prove new regularity results for solutions of first-order partial differential equations of Hamilton-Jacobi type posed as initial value problems on the real line. We show that certain spaces determined by quasinorms related to the solution's approximation properties in C(ℝ) by continuous, piecewise quadratic polynomial functions are invariant under the action of the differential equation. As a result, we show that solutions of Hamilton-Jacobi equations have enough regularity to be approximated well in C(ℝ) by moving-grid finite element methods. The preceding results depend on a new stability theorem for Hamilton-Jacobi equations in any number of spatial dimensions.
2001 ◽
Vol 6
(1)
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pp. 9-19
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Keyword(s):
Keyword(s):
2021 ◽
Vol 1734
◽
pp. 012021
Keyword(s):
2018 ◽
Vol 6
(2)
◽
pp. 53-64
2018 ◽
Vol 14
(5)
◽
pp. 960-969
Keyword(s):
2014 ◽
Vol 2014
◽
pp. 1-7