Strong unique continuation for a class of degenerate elliptic operators
Maejo International Journal of Science and Technology, cilt.20, sa.2, ss.138-152, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 20 Sayı: 2
- Basım Tarihi: 2026
- Dergi Adı: Maejo International Journal of Science and Technology
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Directory of Open Access Journals, Academic Search Ultimate (EBSCO), East & South Asia Database (ProQuest), Natural Science Collection (ProQuest), Biological Science Database (ProQuest), Biomedical Reference Collection: Corporate Edition (EBSCO), Earth, Atmospheric, & Aquatic Science Collection (ProQuest), Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Sayfa Sayıları: ss.138-152
- Anahtar Kelimeler: degenerate elliptic operators, Kato class, partial differential equations, semigroups of operators, unique continuation
- Kırklareli Üniversitesi Adresli: Evet
Özet
The unique continuation property for solutions of second-order elliptic equations has been widely studied owing to its fundamental role in partial differential equations and related fields. While extensive results are available for strictly elliptic operators, comparatively little is known in the degenerate setting. In this paper we establish a strong unique continuation property for a class of degenerate elliptic operators involving potentials in the Kato class. The analysis is carried out under minimal regularity assumptions and the results extend several known contributions in the literature. In particular, we show that solutions that vanish in a neighbourhood, or satisfy appropriate vanishing conditions, must be identically zero. The theoretical findings are further supported by an illustrative example, highlighting the behaviour of solutions and confirming the robustness of the unique continuation property even in the presence of degeneracy and singular potentials.