scientific article; zbMATH DE number 799010

Publication date: 17 April 1996

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

metric spaces Poincaré inequality Sobolev-Poincaré inequality

Metric spaces, metrizability (54E35) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35)

Related Items (99)

Global higher integrability for non-quadratic parabolic quasi-minimizers on metric measure spaces ⋮ A Singular Moser-Trudinger Inequality on Metric Measure Space ⋮ Heat kernel bounds on metric measure spaces and some applications ⋮ Higher integrability for vector-valued parabolic quasi-minimizers on metric measure spaces ⋮ Heat kernel on smooth metric measure spaces and applications ⋮ Hardy-type inequalities derived from \(p\)-harmonic problems ⋮ Convexities of metric spaces ⋮ Lebesgue Points for Orlicz-Sobolev Functions on Metric Measure Spaces ⋮ The obstacle and Dirichlet problems associated with p-harmonic functions in unbounded sets in R^n and metric spaces ⋮ Moser iteration for (quasi)minimizers on metric spaces ⋮ On the regularity of weak contact \(p\)-harmonic maps ⋮ Hölder regularity for parabolic De Giorgi classes in metric measure spaces ⋮ Unnamed Item ⋮ On limits at infinity of weighted Sobolev functions ⋮ A \(T(1)\)-theorem for non-integral operators ⋮ The Hajłasz capacity density condition is self-improving ⋮ Rectifiability of singular sets of noncollapsed limit spaces with Ricci curvature bounded below ⋮ Self-improving properties of John-Nirenberg and Poincaré inequalities on spaces of homogeneous type ⋮ \(\Gamma\)-convergence of nonconvex integrals in Cheeger-Sobolev spaces and homogenization ⋮ Functions of bounded variation on ``good metric spaces ⋮ Finding curves on general spaces through quantitative topology, with applications to Sobolev and Poincaré inequalities ⋮ A note on metric-measure spaces supporting Poincaré inequalities ⋮ Prime ends for domains in metric spaces ⋮ \(\epsilon\)-regularity for shrinking Ricci solitons and Ricci flows ⋮ Lebesgue points for Sobolev functions on metric spaces. ⋮ Existence and uniqueness of limits at infinity for homogeneous Sobolev functions ⋮ BMO, integrability, Harnack and Caccioppoli inequalities for quasiminimizers ⋮ Differentiability of \(p\)-harmonic functions on metric measure spaces ⋮ Uniform Poincaré inequalities on measured metric spaces ⋮ A maximal function approach to two-measure Poincaré inequalities ⋮ Self-improving Poincaré-Sobolev type functionals in product spaces ⋮ Monotonicity formulas for harmonic functions in \(\mathrm{RCD}(0,N)\) spaces ⋮ Relaxation of nonconvex unbounded integrals with general growth conditions in Cheeger-Sobolev spaces ⋮ Lipschitz continuity of Cheeger-harmonic functions in metric measure spaces ⋮ Local Poincaré inequalities from stable curvature conditions on metric spaces ⋮ Local to global results for spaces of BMO type ⋮ Interpolated measures with bounded density in metric spaces satisfying the curvature-dimension conditions of Sturm ⋮ Admissibility versus \(A_p\)-conditions on regular trees ⋮ Elliptic PDEs on Compact Ricci Limit Spaces and Applications ⋮ Gradient estimate for solutions to Poisson equations in metric measure spaces ⋮ Measurability of equivalence classes and MEC\(_p\)-property ⋮ Sobolev space properties of superharmonic functions on metric spaces ⋮ On the Poincaré inequality for vector fields ⋮ Local gradient estimate for harmonic functions on Finsler manifolds ⋮ \(L^p\)-Liouville theorems on complete smooth metric measure spaces ⋮ Nonhomogeneous variational problems and quasi-minimizers on metric spaces ⋮ Local higher integrability for parabolic quasiminimizers in metric spaces ⋮ Alternative proof of Keith–Zhong self-improvement and connectivity ⋮ Volume growth, Green's functions, and parabolicity of ends ⋮ Characterizing spaces satisfying Poincaré inequalities and applications to differentiability ⋮ The boundedness of fractional maximal operators on variable Lebesgue spaces over spaces of homogeneous type ⋮ Generalized doubling meets Poincaré ⋮ Boundedness and differentiability for nonlinear elliptic systems ⋮ Liouville-type theorems for minimal graphs over manifolds ⋮ Weighted Hardy inequalities beyond Lipschitz domains ⋮ Sharp heat kernel bounds and entropy in metric measure spaces ⋮ The Poincaré inequality does not improve with blow-up ⋮ Admissible measures in one dimension ⋮ Collapsed Ricci limit spaces as non-collapsed RCD spaces ⋮ A note on \(p\)-subharmonic functions on complete manifolds ⋮ Riesz transform on manifolds and heat kernel regularity ⋮ Maximal function estimates and self-improvement results for Poincaré inequalities ⋮ Hardy inequalities resulted from nonlinear problems dealing with \(A\)-Laplacian ⋮ New Sobolev spaces via generalized Poincaré inequalities on metric measure spaces ⋮ Uniqueness of weighted Sobolev spaces with weakly differentiable weights ⋮ Weighted inequalities on John domains ⋮ \(p\)-harmonic 1-forms on complete manifolds ⋮ Trudinger inequalities without derivatives ⋮ Harnack's inequality for a nonlinear eigenvalue problem on metric spaces ⋮ Lipschitz continuity of solutions of Poisson equations in metric measure spaces ⋮ On the geometry of metric measure spaces. I ⋮ Convergence to the product of the standard spheres and eigenvalues of the Laplacian ⋮ Lower semicontinuity of multiple µ-quasiconvex integrals ⋮ Locally \(p\)-admissible measures on \(\mathbf{R}\) ⋮ A note on the transition density estimate for some diffusion process on a \(d\)-set ⋮ Morrey-Sobolev spaces on metric measure spaces ⋮ Tensor products and sums of 𝑝\mspace{1𝑚𝑢}-harmonic functions, quasiminimizers and 𝑝\mspace{1𝑚𝑢}-admissible weights ⋮ Existence of parabolic minimizers on metric measure spaces ⋮ Local and semilocal Poincaré inequalities on metric spaces ⋮ Bing meets Sobolev ⋮ A stationary heat conduction problem in low dimensional sets in \({\mathbb{R}}^N\) ⋮ Convergence of non-symmetric diffusion processes on RCD spaces ⋮ Existence of variational solutions to a Cauchy-Dirichlet problem with time-dependent boundary data on metric measure spaces ⋮ A note on local gradient estimate on Alexandrov spaces ⋮ Definitions of Sobolev classes on metric spaces ⋮ Quasiconformal maps in metric spaces with controlled geometry ⋮ Exponentially subelliptic harmonic maps from the Heisenberg group into a sphere ⋮ A new elliptic measure on lower dimensional sets ⋮ Degenerate Poincaré–Sobolev inequalities ⋮ Analysis of weighted p-harmonic forms and applications ⋮ A characterization related to Schrödinger equations on Riemannian manifolds ⋮ Exponential self-improvement of generalized Poincaré inequalities associated with approximations of the identity and semigroups ⋮ Sobolev embedding for \(M^{1, p}\) spaces is equivalent to a lower bound of the measure ⋮ The spectral bound and principal eigenvalues of Schrödinger operators on Riemannian manifolds ⋮ Harmonic functions on asymptotic cones with Euclidean volume growth ⋮ An 𝑛-dimensional space that admits a Poincaré inequality but has no manifold points ⋮ \(L^1\rightarrow L^q\) Poincaré inequalities for \(0<q<1\) imply representation formulas ⋮ Elliptic Theory for Sets with Higher Co-dimensional Boundaries ⋮ Global higher integrability for parabolic quasiminimizers in metric measure spaces

This page was built for publication: