عملگر بیضوی

در ریاضیات، عملگر بیضوی از انواع اصلی عملگرهای دیفرانسیلی است. وجه تمایز این عملگر آن است که ضرایب جملات با مشتق‌های مرتبه بالاتر شرط مثبت بودن را ارضا می‌کنند. معادله گرما و شرودینگر نمونه‌ای از معادلات فیزیکی هستند که شامل عملگر بیضوی می‌باشند.^[۱]

منابع

Evans, L. C. (2010) [1998], Partial differential equations, Graduate Studies in Mathematics, vol. 19 (2nd ed.), Providence, RI: American Mathematical Society, ISBN 978-0-8218-4974-3, MR 2597943 Review:

Rauch, J. (2000). "Partial differential equations, by L. C. Evans" (PDF). Journal of the American Mathematical Society. 37 (3): 363–367. doi:10.1090/s0273-0979-00-00868-5.

Gilbarg, D.; Trudinger, N. S. (1983) [1977], Elliptic partial differential equations of second order, Grundlehren der Mathematischen Wissenschaften, vol. 224 (2nd ed.), Berlin, New York: Springer-Verlag, ISBN 978-3-540-13025-3, MR 0737190
Shubin, M. A. (2001) [1994], "Elliptic operator", Encyclopedia of Mathematics, EMS Press

یادداشت ها

↑ Note that this is sometimes called strict ellipticity, with uniform ellipticity being used to mean that an upper bound exists on the symbol of the operator as well. It is important to check the definitions the author is using, as conventions may differ. See, e.g., Evans, Chapter 6, for a use of the first definition, and Gilbarg and Trudinger, Chapter 3, for a use of the second.

این یک مقالهٔ خرد ریاضیات است. می‌توانید با گسترش آن به ویکی‌پدیا کمک کنید.

[1] Note that this is sometimes called strict ellipticity, with uniform ellipticity being used to mean that an upper bound exists on the symbol of the operator as well. It is important to check the definitions the author is using, as conventions may differ. See, e.g., Evans, Chapter 6, for a use of the first definition, and Gilbarg and Trudinger, Chapter 3, for a use of the second.

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