Describing limits of integrable functions as grid functions of nonstandard analysis

نویسندگان

چکیده

Abstract In functional analysis, there are different notions of limit for a bounded sequence $$L^1$$ L 1 functions. Besides the pointwise limit, that does not always exist, behaviour functions can be described in terms its weak- $$\star $$ ⋆ or by introducing measure-valued notion sense Young measures. Working Robinson’s nonstandard we show every $$\{z_n\}_{n \in \mathbb {N}}$$ { z n } ∈ N exists function hyperfinite domain (i.e. grid function) represents both and measure limits sequence. This result has relevant applications to study nonlinear PDEs. We discuss example an ill-posed forward–backward parabolic equation.

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ژورنال

عنوان ژورنال: Partial Differential Equations And Applications

سال: 2021

ISSN: ['2662-2971', '2662-2963']

DOI: https://doi.org/10.1007/s42985-021-00093-9