Existence and regularity for higher-dimensional \(H\)-systems

DOI10.1215/S0012-7094-00-10133-0zbMath0959.35050OpenAlexW2047597696WikidataQ125599509 ScholiaQ125599509MaRDI QIDQ1975994

Frank Duzaar, Joseph F. Grotowski

Publication date: 26 April 2001

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-00-10133-0

zbMATH Keywords

regularityexistencevariational formulationDirichlet boundary condition\(H\)-systems

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Nonlinear elliptic equations (35J60) Degenerate elliptic equations (35J70) Variational methods for elliptic systems (35J50) Variational problems concerning extremal problems in several variables; Yang-Mills functionals (58E15)

Related Items

A compactness theorem for weak solutions of higher-dimensional \(H\)-systems ⋮ On the H-systems in higher dimension ⋮ The existence of \(G\)-invariant constant mean curvature hypersurfaces ⋮ Global existence and finite time blow‐up for the heat flow of H‐system with constant mean curvature ⋮ The regularity for nonlinear parabolic systems of \(p\)-Laplacian type with critical growth ⋮ EMBEDDED DISC-TYPE SURFACES WITH LARGE CONSTANT MEAN CURVATURE AND FREE BOUNDARIES ⋮ The evolution of \(H\)-surfaces with a Plateau boundary condition ⋮ Total mean curvature of positively curved hypersurfaces ⋮ A global existence result for the heat flow of higher dimensional H-systems ⋮ Weak solutions to the heat flow for surfaces of prescribed mean curvature ⋮ Finite time blow-up for the heat flow of $H$-surface with constant mean curvature

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