STUMMEL CLASSES AND MORREY SPACES AND APPLICATIONS IN STRONG UNIQUE CONTINUATION PROPERTY OF ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS - Kurnia Tumalun, Nicky
Stummel class and Morrey space are the function spaces which play a crucial role, for example, in studying regularity of the elliptic partial differential equations. In 1988, Di Fazio studied an inclusion relation between Stummel class and Morrey space. Since the generalized Stummel spaces were introduced by Eridani and Gunawan in 2005, some authors then studied the inclusion relations between generalized Stummel classes and generalized Morrey spaces. In this dissertation, some proper inclusions between generalized Stummel spaces are obtained. Moreover, the proper inclusion between generalized Stummel classes and generalized Morrey spaces is proved in this research. The parameters condition such that the Lorentz space is contained in the Stummel class, are extended in this research. A function in a bounded Stummel modulus class but does not belong to a Stummel class is given. For applications, the Feffereman inequalities where the potentials belong to a generalized Morrey spaces or a Stummel class, are proved. This results generalize and extend the Fefferman inequalities that were obtained by Fefferman (1983), Zamboni (1987), Chiarenza and Frasca (1990), and Castillo et al (2019). Furthermore, the second order elliptic partial differential equations are shown satisfying the strong unique continuation property by using this Fefferman’s inequality.