Dao động và Tập trung trong Các Chuỗi Đo lường Bị Ràng buộc Bởi PDE

Archive for Rational Mechanics and Analysis - Tập 246 - Trang 823-875 - 2022
Jan Kristensen1, Bogdan Raiță2,3
1Mathematical Institute, University of Oxford, Oxford, UK
2Centro di Ricerca Matematica Ennio de Giorgi, Scuola Normale Superiore, Pisa, Italy
3Department of Mathematics, Alexandru-Ioan Cuza University of Iaşi, Iaşi, Romania

Tóm tắt

Chúng tôi chỉ ra rằng đối với các toán tử vi phân một phần hạng không đổi \(\mathscr {A}\) có các nón sóng trải rộng, các phép đo Young tổng quát sinh ra bởi các chuỗi bị chặn của các phép đo \(\mathscr {A}\)-tự do có thể được đặc trưng bởi sự đối ngẫu với các hàm tích phân \(\mathscr {A}\)-quasi-convex có độ tăng tuyến tính. Điều này bao gồm một đặc trưng về các hiệu ứng tập trung trong các chuỗi như vậy cho phép chúng tôi kết luận rằng, trong sự tương phản rõ rệt với các hiệu ứng dao động, sự tập trung luôn có cấu trúc \(\mathscr {A}\)-tự do.

Từ khóa

#Đo lường Young #toán tử vi phân #tác động tập trung #tác động dao động #tích phân quasi-convex

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