Comparison principles for general potential theories and PDEs
Marco Cirant
Bok · Engelsk · 2023
| Medvirkende | |
|---|---|
| Omfang | xiv, 203 sider
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| Opplysninger | A comprehensive introduction -- Constant-coefficient constraint sets and their subharmonics -- Dirichlet duality and f-subharmonic functions -- Monotonicity cones for constant-coefficient subequations -- A fundamental family of monotonicity cone subequations -- The zero maximum principle for dual monotonicity cones -- The comparison principle for m-monotone subequations -- Comparison on arbitrary domains by additional monotonicity -- Failure of comparison with insufficient maximal monotonicity -- Special cases : reduced constraint sets -- Subequation constraint sets and nonlinear operators -- Comparison principles for nonlinear operators.. - "In this monograph, Cirant et al. prove comparison principles for nonlinear potential theories in Euclidian spaces in a straightforward manner from duality and monotonicity. They also show how to deduce comparison principles for nonlinear differential operators--a program seemingly different from the first. However, this monograph marries these two points of view, for a wide variety of equations, under something called the correspondence principle. Making this connection between potential theory and operator theory enables simplifications on the operator side and provides enrichment on the potential side. Harvey and Lawson have worked for 15 years to articulate a geometric approach to viscosity solutions for an important class of differential equations. Their approach is broader and more flexible than existing alternatives. With the collaboration of Cirant and Payne, this concise book establishes the keystone of the theory: the existence of comparison principles"--
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| Emner | |
| Dewey | |
| ISBN | 9780691243610. - 9780691243627
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