On the convexity of geometric functionals of level for solutions of certain elliptic partial differential equations

DOI10.1007/BF00945002zbMath0679.35026OpenAlexW2094313640WikidataQ115394825 ScholiaQ115394825MaRDI QIDQ1822687

Peter Laurence

Publication date: 1989

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00945002

zbMATH Keywords

convexityisoperimetric inequalitylevel setsp-capacity

Mathematics Subject Classification ID

Second-order elliptic equations (35J15) Qualitative properties of solutions to partial differential equations (35B99)

Related Items (10)

Topology and phase transitions. I: Preliminary results ⋮ Topology and phase transitions. II: Theorem on a necessary relation ⋮ Microcanonical entropy for classical systems ⋮ Isoperimetric inequalities and geometry of level curves of harmonic functions on smooth and singular surfaces ⋮ On the dispute between Boltzmann and Gibbs entropy ⋮ Isoperimetric inequalities and regularity of \(a\)-harmonic functions on surfaces ⋮ Isoperimetric inequalities for the length of level lines of solutions of quasilinear capacity problems in the plane ⋮ Microcanonical entropy and dynamical measure of temperature for systems with two first integrals ⋮ On the variational \(p\)-capacity problem in the plane ⋮ Topological theory of phase transitions

Cites Work

• On surfaces of stationary area bounded by two circles, or convex curves, in parallel planes
• Convexity of solutions of semilinear elliptic equations
• Convex solutions of certain elliptic equations have constant rank Hessians
• Plateau's problem for H-convex curves
• Directional derivative of the increasing rearrangement mapping and application to a queer differential equation in plasma physics
• On extensions of the Brunn-Minkowski and Prekopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation
• Capacitary functions in convex rings
• Starshapedness of Level Sets for the Obstacle Problem and for the Capacitory Potential Problem
• Some Isoperimetric Inequalities for the Level Curves of Capacity and Green’s Functions on Convex Plane Domains
• On minimal surfaces bounded by two convex curves in parallel planes
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