NGHIỆM RENORMALIZED CỦA PHƯƠNG TRÌNH NONLOCAL ELLIPTIC VỚI DỮ LIỆU L^1

Huỳnh Cao Trường, Nguyễn Thanh Long

Tóm tắt


Chúng tôi chứng minh sự tồn tại và duy nhất nghiệm renormalized không âm cho phương trình nonlocal elliptic, là trường hợp tổng quát của phương trình fractional Laplace, với hàm dữ liệu thuộc . Kĩ thuật được sử dụng trong bài báo này là kĩ thuật xấp xỉ dãy nghiệm yếu, thông qua hai bước: Chứng minh sự tồn tại nghiệm yếu của phương trình nonlocal elliptic với hàm dữ liệu  thay cho f (phương pháp chặt cụt); dùng phương pháp xấp xỉ dãy nghiệm yếu trên để thu được nghiệm renormalized.

 


Từ khóa


tồn tại; phương trình nonlocal elliptic; nghiệm renormalized; duy nhất

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DOI: https://doi.org/10.54607/hcmue.js.19.8.3429(2022)

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