Convexity of level curves for an initial value problem

DOI10.1016/0022-247X(88)90404-0zbMath0696.35080MaRDI QIDQ910571

Alan U. Kennington

Publication date: 1988

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

convexityinitial value probleminitial datalevel curvesDirichlet dataconvexity maximum principle

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Maximum principles in context of PDEs (35B50)

Related Items (12)

The Lipschitz continuity of the interface in the heat equation with strong absorption ⋮ Observations on blow up and dead cores for nonlinear parabolic equations ⋮ Parabolic Minkowski convolutions of solutions to parabolic boundary value problems ⋮ A generalization of Caffarelli's contraction theorem via (reverse) heat flow ⋮ Power concavity in weakly coupled elliptic and parabolic systems ⋮ Weak Harnack Inequalities for Eigenvalues and the Monotonicity of Hessian's Rank ⋮ A constant rank theorem for spacetime convex solutions of heat equation ⋮ A microscopic convexity principle for spacetime convex solutions of fully nonlinear parabolic equations ⋮ Geometric properties of superlevel sets of semilinear elliptic equations in convex domains ⋮ On Space-Time Quasiconcave Solutions of the Heat Equation ⋮ On the microscopic spacetime convexity principle of fully nonlinear parabolic equations. I: Spacetime convex solutions ⋮ Parabolic quasi-concavity for solutions to parabolic problems in convex rings

Cites Work

• Convexity of solutions of semilinear elliptic equations
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