Linear Algebra and Its Applications, ISSN 0024-3795, 03/2015, Volume 468, pp. 107 - 121

We consider here the discrete analogue of Serrin's problem: if the equilibrium measure of a network with boundary satisfies that its normal derivative...

Serrin's problem | Minimum principle | Equilibrium measure | Spider networks | Overdetermined boundary value problems | Problems | Overdetermined boundary value | MATHEMATICS | MATHEMATICS, APPLIED | SYMMETRY PROBLEM | BOUNDARY-VALUE-PROBLEMS | EQUATIONS | POTENTIAL-THEORY | NETWORKS | Àlgebra lineal i multilineal | Problema de Serrin | Àlgebra | Matemàtiques i estadística | Àrees temàtiques de la UPC

Serrin's problem | Minimum principle | Equilibrium measure | Spider networks | Overdetermined boundary value problems | Problems | Overdetermined boundary value | MATHEMATICS | MATHEMATICS, APPLIED | SYMMETRY PROBLEM | BOUNDARY-VALUE-PROBLEMS | EQUATIONS | POTENTIAL-THEORY | NETWORKS | Àlgebra lineal i multilineal | Problema de Serrin | Àlgebra | Matemàtiques i estadística | Àrees temàtiques de la UPC

Journal Article

Annali di Matematica Pura ed Applicata (1923 -), ISSN 0373-3114, 8/2016, Volume 195, Issue 4, pp. 1333 - 1345

In a bounded domain $$\varOmega $$ Ω , we consider a positive solution of the problem $$\Delta u+f(u)=0$$ Δ u + f ( u ) = 0 in $$\varOmega $$ Ω , $$u=0$$ u = 0...

Primary 35B06 | Secondary 35B35 | Stability | 35J61 | Method of moving planes | Mathematics | Serrin’s problem | 35J05 | 35B09 | Stationary surfaces | Overdetermined problems | Harnack’s inequality | Mathematics, general | MATHEMATICS | MATHEMATICS, APPLIED | SYMMETRY | Serrin's problem | Harnack's inequality | DOMAINS

Primary 35B06 | Secondary 35B35 | Stability | 35J61 | Method of moving planes | Mathematics | Serrin’s problem | 35J05 | 35B09 | Stationary surfaces | Overdetermined problems | Harnack’s inequality | Mathematics, general | MATHEMATICS | MATHEMATICS, APPLIED | SYMMETRY | Serrin's problem | Harnack's inequality | DOMAINS

Journal Article

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, ISSN 1534-0392, 02/2020, Volume 19, Issue 2, pp. 983 - 1000

... problems, we prove that if the mean curvature H of partial derivative Omega is constant, then Omega is a ball and the unique solution of the Dirichlet p-Laplacian problem is radial...

MATHEMATICS | radial symmetry results | MATHEMATICS, APPLIED | SHAPE | p-torsional problem | STABILITY | Alexandrov's soap bubble theorem | Serrin-type result for overdetermined p-Laplacian problems | P-function | Mathematics - Analysis of PDEs

MATHEMATICS | radial symmetry results | MATHEMATICS, APPLIED | SHAPE | p-torsional problem | STABILITY | Alexandrov's soap bubble theorem | Serrin-type result for overdetermined p-Laplacian problems | P-function | Mathematics - Analysis of PDEs

Journal Article

Kodai mathematical journal, ISSN 0386-5991, 2014, Volume 37, Issue 3, pp. 728 - 736

We consider the solution of the torsion problem−Δu = N in Ω, u = 0 on ∂Ω,where Ω...

Serrin's problem | method of moving planes | overdetermined problems | Parallel surfaces | stability | Serrin’s problem | Stability | Method of moving planes | Overdetermined problems | MATHEMATICS | SYMMETRY

Serrin's problem | method of moving planes | overdetermined problems | Parallel surfaces | stability | Serrin’s problem | Stability | Method of moving planes | Overdetermined problems | MATHEMATICS | SYMMETRY

Journal Article

Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 12/2019, Volume 58, Issue 6, pp. 1 - 12

It is well known that the Serrin condition is a necessary condition for the solvability of the Dirichlet problem for the prescribed mean curvature equation in bounded domains of $${{\,\mathrm{\mathbb {R}}\,}}^n...

53C42 | Serrin condition | Systems Theory, Control | 35J60 | Theoretical, Mathematical and Computational Physics | 49Q05 | Mean curvature equation | Hadamard manifolds | Mathematics | 35J25 | Hyperbolic space | Calculus of Variations and Optimal Control; Optimization | Analysis | Dirichlet problems | Ricci curvature | Radial curvature | Sectional curvature | Laplacian comparison theorem | Distance functions | EXISTENCE | MATHEMATICS, APPLIED | GRAPHS | MATHEMATICS | EQUATION | DOMAINS

53C42 | Serrin condition | Systems Theory, Control | 35J60 | Theoretical, Mathematical and Computational Physics | 49Q05 | Mean curvature equation | Hadamard manifolds | Mathematics | 35J25 | Hyperbolic space | Calculus of Variations and Optimal Control; Optimization | Analysis | Dirichlet problems | Ricci curvature | Radial curvature | Sectional curvature | Laplacian comparison theorem | Distance functions | EXISTENCE | MATHEMATICS, APPLIED | GRAPHS | MATHEMATICS | EQUATION | DOMAINS

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 2009, Volume 70, Issue 2, pp. 1080 - 1086

We prove that if there exists a positive nonconstant function u which is p -harmonic ( 1 < p ⩽ n ) in a punctured domain Ω ∖ { 0 } ⊂ R n and such that both u...

[formula omitted]-function | Round sphere | Free boundary problem | [formula omitted]-Laplacian | p-Laplacian | P-function | MATHEMATICS, APPLIED | POTENTIAL-THEORY | MATHEMATICS | EXTERIOR DOMAINS | RADIAL SYMMETRY | REGULARITY | SERRINS RESULT | DEGENERATE ELLIPTIC-EQUATIONS | DERIVATIVES | RIEMANNIAN-MANIFOLDS

[formula omitted]-function | Round sphere | Free boundary problem | [formula omitted]-Laplacian | p-Laplacian | P-function | MATHEMATICS, APPLIED | POTENTIAL-THEORY | MATHEMATICS | EXTERIOR DOMAINS | RADIAL SYMMETRY | REGULARITY | SERRINS RESULT | DEGENERATE ELLIPTIC-EQUATIONS | DERIVATIVES | RIEMANNIAN-MANIFOLDS

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 05/2018, Volume 75, Issue 9, pp. 3139 - 3146

In this paper, we discuss an overdetermined problem for a weighted Poisson’s equation. We prove that if there exists a solution of the weighted...

Ball | Overdetermined problem | Weighted Laplacian | Mean value properties | MATHEMATICS, APPLIED | RADIAL SYMMETRY | THEOREMS | SERRINS RESULT | BOUNDARY-VALUE-PROBLEMS

Ball | Overdetermined problem | Weighted Laplacian | Mean value properties | MATHEMATICS, APPLIED | RADIAL SYMMETRY | THEOREMS | SERRINS RESULT | BOUNDARY-VALUE-PROBLEMS

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 2007, Volume 57, Issue 5, pp. 1371 - 1377

We describe the family of minimal graphs on strips with boundary values ± ∞ disposed alternately on edges of length 1, and whose conjugate graphs are contained...

Jenkins–Serrin problem | Minimal graph | Periodic minimal surface | Toroidal half-plane layers | KMR examples | Jenkins-Serrin problem | toroidal half-plane layers | MATHEMATICS, APPLIED | minimal graph | PHYSICS, MATHEMATICAL | periodic minimal surface

Jenkins–Serrin problem | Minimal graph | Periodic minimal surface | Toroidal half-plane layers | KMR examples | Jenkins-Serrin problem | toroidal half-plane layers | MATHEMATICS, APPLIED | minimal graph | PHYSICS, MATHEMATICAL | periodic minimal surface

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2012, Volume 393, Issue 2, pp. 489 - 492

Let Ω be a bounded simply connected domain in Rn with connected boundary of class C2. We show that, if there exist n functions satisfying some overdetermined...

Maximum principle | Serrin’s theorem | Overdetermined problem | Serrin's theorem | MATHEMATICS | MATHEMATICS, APPLIED | SYMMETRY PROBLEM | BOUNDARY-VALUE-PROBLEMS | POTENTIAL THEORY

Maximum principle | Serrin’s theorem | Overdetermined problem | Serrin's theorem | MATHEMATICS | MATHEMATICS, APPLIED | SYMMETRY PROBLEM | BOUNDARY-VALUE-PROBLEMS | POTENTIAL THEORY

Journal Article

Applicable analysis, ISSN 0003-6811, 2018, Volume 98, Issue 10, pp. 1785 - 1798

... problem in a bounded star-shaped domain .

overdetermined boundary problems | p-Laplacian | Secondary: 53A10 | p-capacitary potential | Primary: 35N25 | Serrin's overdetermination | Symmetry | Serrin’s overdetermination | CAPACITY | MATHEMATICS, APPLIED | BRUNN-MINKOWSKI INEQUALITY | REGULARITY | BOUNDARY-PROBLEM | Harmonic functions | Domains | Maximum principle | Identities

overdetermined boundary problems | p-Laplacian | Secondary: 53A10 | p-capacitary potential | Primary: 35N25 | Serrin's overdetermination | Symmetry | Serrin’s overdetermination | CAPACITY | MATHEMATICS, APPLIED | BRUNN-MINKOWSKI INEQUALITY | REGULARITY | BOUNDARY-PROBLEM | Harmonic functions | Domains | Maximum principle | Identities

Journal Article

Annali di Matematica Pura ed Applicata, ISSN 0373-3114, 4/2008, Volume 187, Issue 2, pp. 237 - 249

In the theory of linear elliptic problems with data not belonging to H −1 two cases can be distinguished...

35B45 | 35B65 | Mathematics, general | Hölder regularity | Mathematics | Symmetrization methods | 35J25 | Serrin example | MATHEMATICS | MATHEMATICS, APPLIED | symmetrization methods | PARABOLIC EQUATIONS | Holder regularity

35B45 | 35B65 | Mathematics, general | Hölder regularity | Mathematics | Symmetrization methods | 35J25 | Serrin example | MATHEMATICS | MATHEMATICS, APPLIED | symmetrization methods | PARABOLIC EQUATIONS | Holder regularity

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 03/2002, Volume 180, Issue 1, pp. 1 - 50

Existence and uniqueness results for large positive solutions are obtained for a class of quasilinear elliptic eigenvalue problems in general bounded smooth domains via a generalization of a sweeping principle of Serrin...

positive solutions | quasilinear elliptic eigenvalue problems | uniqueness | sweeping principle of Serrin | Positive solutions | Quasilinear elliptic eigenvalue problems | Sweeping principle of Serrin | Uniqueness | EXISTENCE | MAXIMUM PRINCIPLE | 2 SHARP LAYERS | EQUATIONS | NEUMANN PROBLEM | MATHEMATICS | SEMILINEAR DIRICHLET PROBLEM | LEAST-ENERGY SOLUTIONS | GROUND-STATES

positive solutions | quasilinear elliptic eigenvalue problems | uniqueness | sweeping principle of Serrin | Positive solutions | Quasilinear elliptic eigenvalue problems | Sweeping principle of Serrin | Uniqueness | EXISTENCE | MAXIMUM PRINCIPLE | 2 SHARP LAYERS | EQUATIONS | NEUMANN PROBLEM | MATHEMATICS | SEMILINEAR DIRICHLET PROBLEM | LEAST-ENERGY SOLUTIONS | GROUND-STATES

Journal Article

The ANZIAM journal, ISSN 1446-1811, 04/2008, Volume 49, Issue 4, pp. 479 - 494

The aim of this article is to prove a symmetry result for several overdetermined boundary value problems...

Serrin problem | Neumann problem | Compatibility condition | Shape optimization | Overdetermined problem | Mean curvature | Symmetry | MATHEMATICS, APPLIED | overdetermined problem | shape optimization | symmetry | mean curvature | compatibility condition

Serrin problem | Neumann problem | Compatibility condition | Shape optimization | Overdetermined problem | Mean curvature | Symmetry | MATHEMATICS, APPLIED | overdetermined problem | shape optimization | symmetry | mean curvature | compatibility condition

Journal Article

Applied Mathematics Letters, ISSN 0893-9659, 08/2016, Volume 58, pp. 62 - 68

In this article we prove a logarithmic improvement of regularity criteria in the multiplier spaces for the Cauchy problem of the incompressible Navier...

Navier–Stokes | Multiplier spaces | Global regularity | Logarithmic improvement | Pressure | Prodi–Serrin | Navier-Stokes | Prodi-Serrin | Fluid dynamics | Multipliers | Criteria | Mathematical analysis | Regularity | Navier-Stokes equations | Cauchy problem

Navier–Stokes | Multiplier spaces | Global regularity | Logarithmic improvement | Pressure | Prodi–Serrin | Navier-Stokes | Prodi-Serrin | Fluid dynamics | Multipliers | Criteria | Mathematical analysis | Regularity | Navier-Stokes equations | Cauchy problem

Journal Article

Bruno Pini mathematical analysis Seminar, 12/2017, Volume 8, Issue 1, pp. 121 - 141

The distinguished names in the title have to do with different proofs of the celebrated Soap Bubble Theorem and of radial symmetry in certain overdetermined boundary value problems...

quantitative estimates | constant mean curvature | Alexandrov Soap Bubble Theorem | quadrature identities | Serrin's overdetermined problem | integral identities | stability | torsional rigidity

quantitative estimates | constant mean curvature | Alexandrov Soap Bubble Theorem | quadrature identities | Serrin's overdetermined problem | integral identities | stability | torsional rigidity

Journal Article

Journal of optimization theory and applications, ISSN 1573-2878, 2018, Volume 178, Issue 1, pp. 26 - 35

.... Requiring that the torsion function enjoys such a property for the power one half leads to an unconventional overdetermined problem...

35B06 | 52A40 | 35R30 | 35N25 | Mathematics | Theory of Computation | Optimization | Ellipsoids | Optimal concavity | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Applications of Mathematics | Engineering, general | 35R25 | Torsion function | SERRINS | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SYMMETRY | BOUNDARY-VALUE-PROBLEMS | SURFACE | Torsion | Concavity | Analysis of PDEs

35B06 | 52A40 | 35R30 | 35N25 | Mathematics | Theory of Computation | Optimization | Ellipsoids | Optimal concavity | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Applications of Mathematics | Engineering, general | 35R25 | Torsion function | SERRINS | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SYMMETRY | BOUNDARY-VALUE-PROBLEMS | SURFACE | Torsion | Concavity | Analysis of PDEs

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2009, Volume 354, Issue 2, pp. 619 - 624

Let M be a Riemannian manifold such that its geodesic spheres centered at a point a ∈ M are isoperimetric and the distance function dist ( ⋅ , a ) is...

Isoparametric functions | Boundary value problem | Isoperimetric inequality | Overdetermined PDE | SINGULAR SOLUTIONS | MATHEMATICS, APPLIED | BOUNDARY-VALUE-PROBLEMS | SPACE | MATHEMATICS | REGULARITY | SERRINS RESULT | DEGENERATE ELLIPTIC-EQUATIONS | DOMAINS | RIEMANNIAN-MANIFOLDS

Isoparametric functions | Boundary value problem | Isoperimetric inequality | Overdetermined PDE | SINGULAR SOLUTIONS | MATHEMATICS, APPLIED | BOUNDARY-VALUE-PROBLEMS | SPACE | MATHEMATICS | REGULARITY | SERRINS RESULT | DEGENERATE ELLIPTIC-EQUATIONS | DOMAINS | RIEMANNIAN-MANIFOLDS

Journal Article

Complex Variables and Elliptic Equations, ISSN 1747-6933, 06/2012, Volume 57, Issue 6, pp. 653 - 665

If D is a bounded C 1 domain (in ℝ n ) for which the solution to the Dirichlet problem has the property that, for given constants r, l > 0, and for all...

overdetermined problem | Serrin-type problem | symmetry | Primary: 35R35 | EXISTENCE | MATHEMATICS | REGULARITY | FREE-BOUNDARY | POTENTIAL-THEORY | DOMAINS | Problems | Dirichlet problem | Symmetry | Formulations | Consumer goods | Mathematical analysis | Images | Constants | Complex variables

overdetermined problem | Serrin-type problem | symmetry | Primary: 35R35 | EXISTENCE | MATHEMATICS | REGULARITY | FREE-BOUNDARY | POTENTIAL-THEORY | DOMAINS | Problems | Dirichlet problem | Symmetry | Formulations | Consumer goods | Mathematical analysis | Images | Constants | Complex variables

Journal Article

Journal of mathematical fluid mechanics, ISSN 1422-6952, 2015, Volume 18, Issue 1, pp. 25 - 69

In this work, we introduce and study the well-posedness of the multidimensional fractional stochastic Navier–Stokes equations on bounded domains and on the...

58J65 | Fluid- and Aerodynamics | critical | Q-Wiener process | subcritical | pseudo-differential operators | Riesz transform | Fractional stochastic Navier–Stokes equation | global | Faedo–Galerkin approximation | Mathematical Methods in Physics | Serrin’s condition | Beale–Kato–Majda condition | {\gamma}$$ γ -radonifying operators | compactness method | fractional Sobolev spaces | mild | Physics | Classical Continuum Physics | supercritical | local and weak-strong solutions | fractional stochastic vorticity Navier–Stokes equation | Skorokhod embedding theorem | 35R11 | dissipative and hyperdissipative regimes | martingale | 60H15 | UMD Banach spaces of type 2 | (Formula presented.) -radonifying operators | EXISTENCE | Beale-Kato-Majda condition | Faedo-Galerkin approximation | gamma-radonifying operators | Fractional stochastic Navier-Stokes equation | ANALYTICITY | MECHANICS | REGULARITY | INITIAL-VALUE PROBLEM | COEFFICIENTS | Serrin's condition | PHYSICS, FLUIDS & PLASMAS | IMAGINARY POWERS | UNIQUENESS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | UMD BANACH-SPACES | OPERATOR | compactness methods | fractional stochastic vorticity Navier-Stokes equation | Electrical engineering

58J65 | Fluid- and Aerodynamics | critical | Q-Wiener process | subcritical | pseudo-differential operators | Riesz transform | Fractional stochastic Navier–Stokes equation | global | Faedo–Galerkin approximation | Mathematical Methods in Physics | Serrin’s condition | Beale–Kato–Majda condition | {\gamma}$$ γ -radonifying operators | compactness method | fractional Sobolev spaces | mild | Physics | Classical Continuum Physics | supercritical | local and weak-strong solutions | fractional stochastic vorticity Navier–Stokes equation | Skorokhod embedding theorem | 35R11 | dissipative and hyperdissipative regimes | martingale | 60H15 | UMD Banach spaces of type 2 | (Formula presented.) -radonifying operators | EXISTENCE | Beale-Kato-Majda condition | Faedo-Galerkin approximation | gamma-radonifying operators | Fractional stochastic Navier-Stokes equation | ANALYTICITY | MECHANICS | REGULARITY | INITIAL-VALUE PROBLEM | COEFFICIENTS | Serrin's condition | PHYSICS, FLUIDS & PLASMAS | IMAGINARY POWERS | UNIQUENESS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | UMD BANACH-SPACES | OPERATOR | compactness methods | fractional stochastic vorticity Navier-Stokes equation | Electrical engineering

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 2008, Volume 244, Issue 11, pp. 2741 - 2763

We first represent the pressure in terms of the velocity in R + 3 . Using this representation we prove that a solution to the Navier–Stokes equations is in L ∞...

Prodi–Ohyama–Serrin–Ladyzhenskaya condition | Navier–Stokes equations | Boundary regularity | Moser iteration | Pressure representation | Slip boundary condition | Navier-Stokes equations | Prodi-Ohyama-Serrin-Ladyzhenskaya condition | MATHEMATICS | boundary regularity | pressure representation | SYSTEMS | slip boundary condition | INITIAL-VALUE-PROBLEM | WEAK SOLUTIONS

Prodi–Ohyama–Serrin–Ladyzhenskaya condition | Navier–Stokes equations | Boundary regularity | Moser iteration | Pressure representation | Slip boundary condition | Navier-Stokes equations | Prodi-Ohyama-Serrin-Ladyzhenskaya condition | MATHEMATICS | boundary regularity | pressure representation | SYSTEMS | slip boundary condition | INITIAL-VALUE-PROBLEM | WEAK SOLUTIONS

Journal Article

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