Stable solutions are ubiquitous in differential equations. They
represent meaningful solutions from a physical point of view and
appear in many applications, including mathematical physics
(combustion, phase transition theory) and geometry (minimal
surfaces). Stable Solutions of Elliptic Partial Differential
Equations offers a self-contained presentation of the notion of
stability in elliptic partial differential equations (PDEs). The
central questions of regularity and classification of stable
solutions are treated at length. Specialists will find a summary of
the most recent developments of the theory, such as nonlocal and
higher-order equations. For beginners, the book walks you through
the fine versions of the maximum principle, the standard regularity
theory for linear elliptic equations, and the fundamental
functional inequalities commonly used in this field. The text also
includes two additional topics: the inverse-square potential and
some background material on submanifolds of Euclidean space.
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