Elliptic theory in domains with boundaries of mixed dimension - David, Guy; Feneuil, Joseph; Mayboroda, Svitlana (Paris: Societe Mathhematique De France, 2023)
Motivation and a general overview of the main results -- Our assumptions -- Some examples where our assumptions hold -- The definition of the space W -- The access cones and their properties -- The trace theorem -- Poincare inequalities on the boundary -- The extension theorem -- Completeness of W and density of smooth functions -- The localized versions Wr (E) of our energy space W -- Definitions of solutions and their properties -- Construction of the harmonic measure -- Bounded boundaries -- Green functions -- Comparison principle
Includes bibliography
Keywords: Mathematics -- Analysis; Elliptic Theory; Operator Theory; Elliptic Operators; Inequalities on Boundary