Weak solutions to the heat flow for surfaces of prescribed mean curvature
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Publication:2847120
DOI10.1090/S0002-9947-2013-05885-0zbMath1293.53009MaRDI QIDQ2847120
Christoph Scheven, Verena Bögelein, Frank Duzaar
Publication date: 4 September 2013
Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)
Asymptotic behavior of solutions to PDEs (35B40) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Initial-boundary value problems for second-order parabolic systems (35K51)
Related Items (5)
Discrete Morse Flow for Yamabe Type Heat Flows ⋮ On the heat flow of equation of \(H\)-surface ⋮ The discrete Morse flow method for parabolic \(p\)-Laplacian systems ⋮ Global existence and finite time blow‐up for the heat flow of H‐system with constant mean curvature ⋮ The evolution of \(H\)-surfaces with a Plateau boundary condition
Cites Work
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- A global existence result for the heat flow of higher dimensional H-systems
- Regularity of polyharmonic maps in the critical dimension
- Existence and uniqueness of weak solutions for a non-uniformly parabolic equation
- On the evolution of harmonic mappings of Riemannian surfaces
- Compact sets in the space \(L^ p(0,T;B)\)
- The existence of surfaces of constant mean curvature with free boundaries
- Heat flow for the equation of surfaces with prescribed mean curvature
- On the existence of surfaces with prescribed mean curvature and boundary
- Isoperimetric inequalities and the problem of Plateau
- A selection lemma for sequences of measurable sets, and lower semicontinuity of multiple integrals
- Parametric surfaces of least \(H\)-energy in a Riemannian manifold
- The existence of the heat flow of \(H\)-systems.
- Construction of harmonic map flows through the method of discrete Morse flows
- Existence and regularity for higher-dimensional \(H\)-systems
- Conservation laws for conformally invariant variational problems
- Zu einem Satz von S. Hildebrandt über das Randverhalten der Minimalflächen
- Randwertprobleme für Flächen mit vorgeschriebener mittlerer Krümmung und Anwendungen auf die Kapillaritätstheorie. I: Fest vorgegebener Rand
- Ein einfacher Beweis eines Regularitätssatzes für schwache Lösungen gewisser elliptischer Systeme
- An existence theorem for surfaces of constant mean curvature
- Einige Bemerkungen über Flächen beschränkter mittlerer Krümmung. (Some remarks about surfaces of bounded mean curvature)
- The Plateau problem for surfaces of prescribed mean curvature in a cylinder
- Second order parabolic systems, optimal regularity, and singular sets of solutions
- Über die Existenz einer Fläche konstanter mittlerer Krümmung bei vorgegebener Berandung
- Weak solutions of a biharmonic map heat flow
- Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105)
- Variational inequalities and harmonic mappings.
- Existence of hypersurfaces with prescribed mean curvature in Riemannian manifolds
- Two‐dimensional variational problems with obstructions, and Plateau's problem for h‐surfaces in a riemannian manifold
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