A stationary heat conduction problem in low dimensional sets in RN

• Published in: Calculus of variations and partial differential equations Vol. 59; no. 1
• Main Authors: Rybka, Piotr, Zatorska-Goldstein, Anna
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 2020; Springer Nature B.V
• Subjects: Analysis; Boundary conditions; Calculus of Variations and Optimal Control; Optimization; Conduction heating; Conductive heat transfer; Control; Mathematical and Computational Physics; Mathematics; Mathematics and Statistics; Systems Theory; Theoretical; 28A33; 35J20; 35J70

We study a basic linear elliptic equation on a lower dimensional rectifiable set S in R N with the Neumann boundary data. Set S is a support of a finite Borel measure μ . We will use the measure theoretic tools to interpret the equation and the Neumann boundary condition. For this purpose we recall...