Oblique Derivative Problems for Elliptic Equations in Conical Domains

​Professor Mikhail Borsuk is a well-known specialist in nonlinear boundary value problems for elliptic equations in non-smooth domains. He is a student-follower of eminent mathematicians Y. B. Lopatinskiy and V. A. Kondratiev. He graduated at the Steklov Mathematical Institute of the Russian Academy of Sciences (Moscow) for his postgraduate studies and then worked at the Moscow Institute of Physics and Technology and at the Central Aeroрydrodynamic Institute of Professor N. E. Zhukovskiy. Currently he is professor emeritus at the University of Warmia and Mazury in Olsztyn (Poland), here he worked for more than 20 years. He has published 3 monographs, 2 textbooks for students and about 80 scientific articles.

• - 1. Introduction. - 2. Preliminaries. - 3. Eigenvalue Problems. - 4. Integral Inequalities. - 5. The Linear Oblique Derivative Problem for Elliptic Second Order Equation in a Domain with Conical Boundary Point. - 6. The Oblique Derivative Problem for Elliptic Second Order Semi-linear Equations in a Domain with a Conical Boundary Point. - 7. Behavior of Weak Solutions to the Conormal Problem for Elliptic Weak Quasi-Linear Equations in a Neighborhood of a Conical Boundary Point. - 8. Behavior of Strong Solutions to the Degenerate Oblique Derivative Problem for Elliptic Quasi-linear Equations in a Neighborhood of a Boundary Conical Point. - 9. The Oblique Derivative Problem in a Plane Sector for Elliptic Second Order Equation with Perturbed p(x)-Laplacian. - 10. The Oblique Derivative Problem in a Bounded n-Dimensional Cone for Strong Quasi-Linear Elliptic Second Order Equation with Perturbed p(x)-Laplacian. - 11. Existence of Bounded Weak Solutions.

“The book under review presents a comprehensive and meticulously structured exploration of strong and weak solutions concerning regular oblique derivative problems for second-order elliptic equations. Its systematic approach and detailed examination of boundary singularities make it a valuable resource for researchers and practitioners in various fields … . Its comprehensive treatment, structured approach, and detailed analysis make it an indispensable resource for postgraduates and young researchers seeking to deepen their understanding of elliptic equations within conical domains.” (Giuseppe Di Fazio, zbMATH 1532.35001, 2024)