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- W2883629325 abstract "We consider the strictly hyperbolic Cauchy problem $$displaystyle begin {cases} D_t^m u - sum limits _{j = 0}^{m-1} sum limits _{|gamma |+j = m} a_{m-j,,gamma }(t,,x) D_x^gamma D_t^j u = 0, D_t^{k-1}u(0,,x) = g_k(x),,k = 1,,ldots ,,m, end {cases} $$ for $$(t,,x) in [0,,T]times mathbb {R}^n$$ with coefficients belonging to the Zygmund class $$C_ast ^s$$ in x and having a modulus of continuity below Lipschitz in t. Imposing additional conditions to control oscillations, we obtain a global (on [0, T]) L 2 energy estimate without loss of derivatives for $$s geq max {1+varepsilon ,,frac {2m_0}{2-m_0}}$$ , where m 0 is linked to the modulus of continuity of the coefficients in time." @default.
- W2883629325 created "2018-08-03" @default.
- W2883629325 creator A5041305044 @default.
- W2883629325 date "2020-01-01" @default.
- W2883629325 modified "2023-09-24" @default.
- W2883629325 title "Strictly Hyperbolic Cauchy Problems with Coefficients Low-Regular in Time and Space" @default.
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- W2883629325 doi "https://doi.org/10.1007/978-3-030-36138-9_19" @default.
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