Uniqueness results for some PDEs | Zendy

Nader Masmoudi | Zendy

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Uniqueness results for some PDEs

Author(s) -

Nader Masmoudi

Publication year - 2003

Publication title -

journées équations aux dérivées partielles

Language(s) - English

Resource type - Journals

eISSN - 2118-9366

pISSN - 0752-0360

DOI - 10.5802/jedp.624

Subject(s) - uniqueness , argument (complex analysis) , mathematics , banach space , duality (order theory) , class (philosophy) , fixed point , space (punctuation) , pure mathematics , mathematical analysis , computer science , epistemology , philosophy , biochemistry , chemistry , operating system

Existence of solutions to many kinds of PDEs can be proved by using a fixed point argument or an iterative argument in some Banach space. This usually yields uniqueness in the same Banach space where the fixed point is performed. We give here two methods to prove uniqueness in a more natural class. The first one is based on proving some estimates in a less regular space. The second one is based on a duality argument. In this paper, we present some results obtained in collaboration with Pierre-Louis Lions, with Kenji Nakanishi and with Fabrice Planchon.

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