Shorter Notes: Regularity of the Distance Function

From MaRDI portal
Publication:3310519

DOI10.2307/2045171zbMath0528.53005OpenAlexW2055705334MaRDI QIDQ3310519

Robert L. Foote

Publication date: 1984

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2045171




Related Items

On the moving plane method for singular solutions to semilinear elliptic equationsStationary solutions to a compressible non-Newtonian fluid with general boundary conditionsA new parameter free partially penalized immersed finite element and the optimal convergence analysisQuantum confinement on non-complete Riemannian manifoldsA minimising movement scheme for the \(p\)-elastic energy of curvesOn the extremal function of the modulus of a foliationRegularity results for solutions to the \(c\)-Plateau problem with free boundary having small singular set, and generally in codimension zeroPartial regularity for holonomic minimisers of quasiconvex functionalsCompensated Convexity, Multiscale Medial Axis Maps and Sharp Regularity of the Squared-Distance FunctionThe singular perturbation problem for a class of generalized logistic equations under non-classical mixed boundary conditionsOn the mass of static metrics with positive cosmological constant: IEuler system with a polytropic equation of state as a vanishing viscosity limitDifferential geometry of real Monge-Ampère foliationsAn immersed Raviart-Thomas mixed finite element method for elliptic interface problems on unfitted meshesRicci DeTurck flow on incomplete manifoldsCoercivity of Combined Boundary Integral Equations in High-Frequency ScatteringBoundary estimation from point clouds: algorithms, guarantees and applicationsTwo-phase compressible/incompressible Navier-Stokes system with inflow-outflow boundary conditionsWasserstein stability of porous medium-type equations on manifolds with Ricci curvature bounded belowUnnamed ItemReaction-diffusion on metric graphs: from 3D to 1DStationary solutions to the compressible Navier-Stokes system with general boundary conditionsCurvature and distance function from a manifoldDeformation of scalar curvature and volumeA cell-cell repulsion model on a hyperbolic Keller-Segel equationAn immersed \(CR\)-\(P_0\) element for Stokes interface problems and the optimal convergence analysisConvergence of a Brinkman-type penalization for compressible fluid flowsAnalysis of nonconforming IFE methods and a new scheme for elliptic interface problemsLocalized nodal solutions for a critical nonlinear Schrödinger equationDistance from submanifolds with boundary and applications to Poincaré inequalities and to elliptic and parabolic problemsCompressible Navier‐Stokes system with general inflow‐outflow boundary data on piecewise regular domainsRigidity of nonpositively curved manifolds with convex boundaryConvergence of the Euler-Maruyama method for multidimensional SDEs with discontinuous drift and degenerate diffusion coefficientUniqueness and support properties of solutions to singular quasilinear parabolic equations on surfaces of revolutionIterative Computation of the Fréchet Derivative of the Polar DecompositionA nonconforming immersed virtual element method for elliptic interface problemsNavigating Around Convex SetsA compactness result about density in compressible Navier-Stokes equations in variable domainAn immersed Crouzeix-Raviart finite element method in 2D and 3D based on discrete level set functionsA new numerical scheme for discrete constrained total variation flows and its convergenceCompressible Navier-Stokes system with hard sphere pressure law and general inflow-outflow boundary conditionsExistence, uniqueness and structure of second order absolute minimisersDelay embedding of periodic orbits using a fixed observation functionAmbient residual penalty approximation of partial differential equations on embedded submanifoldsAmbient approximation on embedded submanifoldsOn support of solutions to singular nonlinear parabolic equations in bounded domainsCompressible Navier--Stokes System with General Inflow-Outflow Boundary DataShort time uniqueness results for solutions of nonlocal and non-monotone geometric equationsPositive solutions of semilinear elliptic problems with a Hardy potentialOn the Höpf boundary lemma for singular semilinear elliptic equationsExistence, uniqueness and regularity of the projection onto differentiable manifoldsSymmetry and scaling limits for matching of implicit surfaces based on thin shell energiesCriteria for well-posedness of degenerate elliptic and parabolic problemsPropagation of regularity of level sets for a class of active transport equationsDiffusion processes in thin tubes and their limits on graphsThe \(c\)-isoperimetric mass of currents and the \(c\)-Plateau problemGeneralized shape operators on polyhedral surfacesA priori estimates and theory of existence for parabolic equations in variable Hölder spacesFast computation of weighted distance functions and geodesics on implicit hyper-surfacesOn the Höpf boundary lemma for quasilinear problems involving singular nonlinearities and applicationsA narrow-band unfitted finite element method for elliptic PDEs posed on surfacesEnergy and cross-helicity conservation for the three-dimensional ideal MHD equations in a bounded domainFree boundary minimal surfaces in the unit three-ball via desingularization of the critical catenoid and the equatorial discThe distance from the boundary in a Riemannian manifold: regularity up to a conformal change of the metricUniqueness and non-uniqueness of bounded solutions to singular nonlinear parabolic equationsConstruction of weak solutions to compressible Navier-Stokes equations with general inflow/outflow boundary conditions via a numerical approximationThe simultaneous asymmetric perturbation method for overdetermined free boundary problemsPenalty method for obliquely reflected diffusionsGinzburg-Landau relaxation for harmonic maps on planar domains into a general compact vacuum manifoldTotal curvature and the isoperimetric inequality in Cartan-Hadamard manifoldsSparse data interpolation and smoothing on embedded submanifoldsSingular measure traveling waves in an epidemiological model with continuous phenotypesFast diffusion on noncompact manifolds: Well-posedness theory and connections with semilinear elliptic equationsSchauder theory in variable Hölder spaces