Lower Semicontinuity, Existence and Regularity Theorems for Elliptic Variational Integrals of Multiple Valued Functions

DOI10.2307/1999635zbMath0539.49010OpenAlexW4255000058MaRDI QIDQ3326324

Pertti Mattila

Publication date: 1983

Full work available at URL: https://doi.org/10.2307/1999635

zbMATH Keywords

generalized Dirichlet integralQ-elliptic integralsQ-valued minimizing function

Mathematics Subject Classification ID

Set-valued functions (26E25) Set-valued maps in general topology (54C60) Weak and generalized continuity (54C08) Variational problems in a geometric measure-theoretic setting (49Q20) Methods involving semicontinuity and convergence; relaxation (49J45) Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Length, area, volume, other geometric measure theory (28A75) Integral geometry (53C65) Special properties of functions of several variables, Hölder conditions, etc. (26B35) Currents in global analysis (58A25)

Related Items (7)

A multiple-valued plateau problem ⋮ Interior continuity of two-dimensional weakly stationary-harmonic multiple-valued functions ⋮ 𝑄-valued functions revisited ⋮ Regular selections for multiple-valued functions ⋮ Multiple valued maps into a separable Hilbert space that almost minimize their \(p\) Dirichlet energy or are squeeze and squash stationary ⋮ Rectifiability of the singular set of multiple-valued energy minimizing harmonic maps ⋮ Multi-value microstructural descriptors for complex materials: analysis of ground states

Cites Work

• Existence and regularity almost everywhere of solutions to elliptic variational problems among surfaces of varying topological type and singularity structure
• Elliptic Partial Differential Equations of Second Order
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