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Journal of Geometry, ISSN 0047-2468, 8/2018, Volume 109, Issue 2, pp. 1 - 7
A set $$E \subset \mathbb {R}^n$$ E⊂Rn is called uniformly discrete if there exists an $$\varepsilon >0 $$ ε>0 such that no two points of E are closer than... 
paradoxical sets | 28C10 | Mathematics | Geometry | discrete groups | Secondary 03E05 | sets with removable points | 20H15 | 22E40 | Primary 51M05 | 20E05 | finitely additive isometry-invariant measures | Congruence of sets
Journal Article
Nonlinear Differential Equations and Applications NoDEA, ISSN 1021-9722, 4/2018, Volume 25, Issue 2, pp. 1 - 12
Our main result in this note can be stated as follows: Assume $$E\subset B_{1}$$ E⊂B1 and 0.1$$\begin{aligned} F(D^2u(x),\nabla u(x), u(x),x) \le \psi (x)\... 
Removable sets | 35J62 | Fully nonlinear | 35J60 | Analysis | 35B65 | Mathematics | 35R35 | 35J25 | Degenerate equations | VISCOSITY SOLUTIONS | MATHEMATICS, APPLIED | MAXIMUM PRINCIPLE | SINGULARITIES | EQUATIONS | OPERATORS
Journal Article
Sbornik Mathematics, ISSN 1064-5616, 2017, Volume 208, Issue 7, pp. 1073 - 1086
The sufficiency of several conditions for the removability of singularities is proved for complex analytic sets in domains in C-n. 
Rational convexity | Complex analytic sets | Removable singularities | rational convexity | MATHEMATICS | removable singularities | complex analytic sets | Singularities | Mathematics - Complex Variables
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 07/2014, Volume 415, Issue 2, pp. 803 - 815
In the present article we provide a sufficient condition for a closed set F∈Rd to have the following property which we call c-removability: Whenever a... 
Locally convex function | Convex extension | Convex function | c-removable set | Intervally thin set | Separately convex function | C-removable set | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 03/2019, Volume 266, Issue 7, pp. 4061 - 4105
We consider the heat equation with a superlinear absorption term ∂tu−Δu=−up in Rn and study the existence of nonnegative solutions with an m-dimensional... 
Higher dimensional singular set | Time-dependent singularity | Semilinear heat equation | Singular solution | MATHEMATICS | REMOVABLE SINGULARITIES
Journal Article
Computational Methods and Function Theory, ISSN 1617-9447, 9/2019, Volume 19, Issue 3, pp. 473 - 486
In this paper, we provide a concrete criterion for sets lying in a hyperplane to be removable for weighted Orlicz–Sobolev spaces. We define porous sets and... 
Removable sets | Weighted orlicz–sobolev spaces | Computational Mathematics and Numerical Analysis | Functions of a Complex Variable | Analysis | Mathematics | Porosity | 31B15 | MATHEMATICS | Weighted orlicz-sobolev spaces | MATHEMATICS, APPLIED | THEOREMS
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 04/2015, Volume 424, Issue 2, pp. 1296 - 1322
We prove the existence and continuity of solutions to obstacle problems with p(x)-type nonstandard growth, and establish the conditions of removability of... 
Removable set | Hausdorff measure | Variable exponent space | OBSTACLE PROBLEM | MATHEMATICS | MATHEMATICS, APPLIED | SPACES
Journal Article
Potential Analysis, ISSN 0926-2601, 11/2015, Volume 43, Issue 4, pp. 675 - 694
We study removable sets for the Orlicz-Sobolev space W 1,Ψ, for functions of the form Ψ ( t ) = t p log λ ( e + t ) ${\Psi }(t)=t^{p}\log ^{\lambda }(e+t)$ .... 
Geometry | Removable sets | Potential Theory | Functional Analysis | Orlicz-Sobolev spaces | Probability Theory and Stochastic Processes | Mathematics | Porosity | 31B15 | MATHEMATICS
Journal Article
American Journal of Mathematics, ISSN 0002-9327, 2016, Volume 138, Issue 2, pp. 499 - 527
This paper deals with some geometrical properties of solutions of some semilinear elliptic equations in bounded convex domains or convex rings. Constant... 
Differential equations, Elliptic | Convex sets | Convex domains | Rings (Algebra) | DIRICHLET PROBLEMS | EIGENVALUE | MATHEMATICS | MAXIMUM PRINCIPLE | PARTIAL-DIFFERENTIAL-EQUATIONS | BOUNDARY-VALUE-PROBLEMS | QUASICONCAVE SOLUTIONS | POWER CONCAVITY | NONCONVEXITY | REMOVABLE SINGULARITIES | UNIQUENESS | Analysis | Geometry | Linear equations | Analysis of PDEs | Mathematics
Journal Article
Annali di Matematica Pura ed Applicata (1923 -), ISSN 0373-3114, 2/2018, Volume 197, Issue 1, pp. 41 - 59
This paper establishes removable singularity theorems for nonnegative continuous solutions of quasilinear elliptic equations with nonlinear source or... 
Nonlinear potential estimate | Secondary 31C45 | 28A80 | Mathematics, general | Fractal set | Mathematics | Primary 35J92 | Removable singularity | Quasilinear elliptic equation | Iteration method | SINGULAR SOLUTIONS | MATHEMATICS | MATHEMATICS, APPLIED | BEHAVIOR | HESSIAN EQUATIONS
Journal Article
Functional Analysis and Its Applications, ISSN 0016-2663, 1/2018, Volume 52, Issue 1, pp. 62 - 65
It is shown that, for any compact set K ⊂ ℝ n (n ⩾ 2) of positive Lebesgue measure and any bounded domain G ⊃ K, there exists a function in the Hölder class C... 
Schauder theorem | nonlinear mapping | minimal surface equation | Functional Analysis | Hölder class | fixed point | Analysis | Mathematics | removable set | Holder class | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Georgian Mathematical Journal, ISSN 1072-947X, 12/2015, Volume 22, Issue 4, pp. 509 - 528
In this paper we give a direct generalization of Carleson–Ullrich's theorem in Besov spaces and geometric characterization of removable sets for harmonic... 
harmonic function | singularity | 30H25 | 31B05 | Besov space | removable set | MATHEMATICS
Journal Article
Mathematische Annalen, ISSN 0025-5831, 4/2013, Volume 355, Issue 4, pp. 1349 - 1381
We extend the theory of the thermal capacity for the heat equation to nonlinear parabolic equations of the $$p$$ -Laplacian type. We study definitions and... 
Mathematics, general | Mathematics | 31C45 | 35K55 | MATHEMATICS | EQUATIONS | BOUNDARY | BEHAVIOR | SEMICONTINUOUS SUPERSOLUTIONS | REMOVABLE SINGULARITIES
Journal Article
Commentarii Mathematici Helvetici, ISSN 0010-2571, 2014, Volume 89, Issue 2, pp. 405 - 441
In this article, we prove several results about the extension to the boundary of conformal immersions from an open subset $\Omega$ of a Riemannian manifold $L$... 
Differential geometry | Removable sets | Conformal mappings | MATHEMATICS | MANIFOLDS | THEOREM | removable sets | QUASI-REGULAR MAPPINGS
Journal Article
Siberian Mathematical Journal, ISSN 0037-4466, 10/2009, Volume 50, Issue 5, pp. 760 - 775
Journal Article
Complex Variables and Elliptic Equations, ISSN 1747-6933, 02/2016, Volume 61, Issue 2, pp. 151 - 165
Using Moser's iteration method, we obtain the removability of compact singular sets with capacity zero under some conditions for nonlinear elliptic equations... 
variable exponent spaces | removable singularity | 35J60 | 35B60 | singular sets | Variable exponent spaces | Singular sets | Removable singularity | MATHEMATICS | SPACES | NONSTANDARD GROWTH | ELECTRORHEOLOGICAL FLUIDS | Nonlinearity | Complex variables | Exponents | Sobolev space | Mathematical analysis
Journal Article
Turkish Journal of Mathematics, ISSN 1300-0098, 2014, Volume 38, Issue 2, pp. 311 - 317
In this paper for 1 <= p < infinity we introduce a space A(p) (Omega\K) of all functions u is an element of b(p) (Omega\K) such that there exist v is an... 
Reproducing kernel | Bergman spaces | Removable singularity | Harmonic function | MATHEMATICS | harmonic function | removable singularity | reproducing kernel
Journal Article
Zeitschrift fur Analysis und ihre Anwendung, ISSN 0232-2064, 2011, Volume 30, Issue 4, pp. 421 - 433
We establish in this paper that sets of m-Hausdorff measure zero are removable for C-0,C-alpha A-harmonic functions with m depending only on n, alpha and A.... 
Orlicz Sobolev spaces | Removable sets | Hausdorff measure | Hölder continuity | A-Laplacian | MATHEMATICS | Holder continuity | MATHEMATICS, APPLIED | INEQUALITIES | removable sets | LINEAR ELLIPTIC-EQUATIONS | ORLICZ SPACES
Journal Article
Journal of Prosthodontics, ISSN 1059-941X, 10/2008, Volume 17, Issue 7, pp. 515 - 516
Journal Article
HOKKAIDO MATHEMATICAL JOURNAL, ISSN 0385-4035, 2016, Volume 45, Issue 2, pp. 195 - 222
We investigate removable sets for subcaloric functions satisfying either a growth condition or an integrability condition by defining suitably upper Minkowski... 
MATHEMATICS | Hausdorff measure | caloric function | PARABOLIC EQUATIONS | semilinear heat equation | SINGULARITIES | NONLINEAR ELLIPTIC-EQUATIONS | removable singularity | subcaloric function | Minkowski content | SUBHARMONIC FUNCTIONS
Journal Article
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