The prescribed mean curvature equation in weakly regular domains
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Publication:1635640
DOI10.1007/s00030-018-0500-3zbMath1391.49041arXiv1606.04828OpenAlexW3104469151WikidataQ130199323 ScholiaQ130199323MaRDI QIDQ1635640
Giorgio Saracco, Gian Paolo Leonardi
Publication date: 31 May 2018
Published in: NoDEA. Nonlinear Differential Equations and Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1606.04828
Optimality conditions for problems involving partial differential equations (49K20) Variational problems in a geometric measure-theoretic setting (49Q20) Quasilinear elliptic equations with mean curvature operator (35J93)
Related Items (23)
Rigidity and trace properties of divergence-measure vector fields ⋮ On smooth interior approximation of sets of finite perimeter ⋮ On BV functions and essentially bounded divergence-measure fields in metric spaces ⋮ Weighted Cheeger sets are domains of isoperimetry ⋮ Representation formulas for pairings between divergence-measure fields and \(BV\) functions ⋮ The Cheeger constant of a Jordan domain without necks ⋮ Extensions and traces of BV functions in rough domains and generalized Cheeger sets ⋮ A sufficient criterion to determine planar self-Cheeger sets ⋮ The Cheeger problem in abstract measure spaces ⋮ Anzellotti's pairing theory and the Gauss-Green theorem ⋮ An extension of the pairing theory between divergence-measure fields and BV functions ⋮ Cauchy fluxes and Gauss-Green formulas for divergence-measure fields over general open sets ⋮ Two examples of minimal Cheeger sets in the plane ⋮ The Gauss-Green theorem in stratified groups ⋮ Rough traces of BV functions in metric measure spaces ⋮ Quantitative lower bounds to the Euclidean and the Gaussian Cheeger constants ⋮ Positive solutions of the prescribed mean curvature equation with exponential critical growth ⋮ The Dirichlet problem for a prescribed mean curvature equation ⋮ A discrete districting plan ⋮ Dimensional lower bounds for contact surfaces of Cheeger sets ⋮ Pairings between bounded divergence-measure vector fields and BV functions ⋮ Minimizers of the prescribed curvature functional in a Jordan domain with no necks ⋮ The isoperimetric problem in 2d domains without necks
Cites Work
- On the Cheeger sets in strips and non-convex domains
- BV supersolutions to equations of 1-Laplace and minimal surface type
- One-sided approximation of sets of finite perimeter
- A strict maximum principle for area minimizing hypersurfaces
- The Gauss--Green theorem and removable sets for PDEs in divergence form
- A proof of the Concus-Finn conjecture
- Cauchy flux and sets of finite perimeter
- Traces and fine properties of a \(BD\) class of vector fields and applications
- Capillary drops: contact angle hysteresis and sticking drops
- Area, coarea, and approximation in \(W^{1,1}\)
- Pairings between measures and bounded functions and compensated compactness
- Regularity of capillary surfaces over domains with corners: Borderline case
- On existence criteria for capillary free surfaces without gravity
- Non-uniqueness and uniqueness of capillary surfaces
- Funzioni BV e tracce
- Existence, regularity, and boundary behaviour of generalized surfaces of prescribed mean curvature
- Superfici di curvatura media assegnata con ostacolo
- On capillary free surfaces in the absence of gravity
- On capillary free surfaces in a gravitational field
- On the equation of surfaces of prescribed mean curvature. Existence and uniqueness without boundary conditions
- Divergence-measure fields and hyperbolic conservation laws
- On the Dirichlet problem for surfaces of prescribed mean curvature
- Extended divergence-measure fields and the Euler equations for gas dynamics
- Anzellotti's pairing theory and the Gauss-Green theorem
- Two examples of minimal Cheeger sets in the plane
- Divergence-measure fields, sets of finite perimeter, and conservation laws
- Rigidity and trace properties of divergence-measure vector fields
- On locally essentially bounded divergence measure fields and sets of locally finite perimeter
- Regularity of free boundaries in anisotropic capillarity problems and the validity of Young's law
- Convex duality and uniqueness for BV-minimizers
- Remarks relevant to minimal surfaces and to surfaces of prescribed mean curvature
- Sets of Finite Perimeter and Geometric Variational Problems
- A Note on the Gauss-Green Theorem
- An Overview on the Cheeger Problem
- THE GAUSS–GREEN THEOREM IN THE CONTEXT OF LEBESGUE INTEGRATION
- Strict interior approximation of sets of finite perimeter and functions of bounded variation
- Gauss‐Green theorem for weakly differentiable vector fields, sets of finite perimeter, and balance laws
- ON THE BEHAVIOR OF A CAPILLARY SURFACE IN A WEDGE
- Sobolev Spaces
- Exotic containers for capillary surfaces
- The Gauss-Green Theorem
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