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2016, Graduate studies in mathematics, ISBN 9781470426071, Volume 171., viii, 368

Differential equations, Elliptic | Boundary value problems for second-order elliptic equations | Partial differential equations | Differential equations, Nonlinear | Elliptic equations and systems | Quasilinear elliptic equations with mean curvature operator | Elliptic Monge-Ampère equations | Nonlinear elliptic equations

Book

Journal of mathematical analysis and applications, ISSN 0022-247X, 09/2013, Volume 405, Issue 1, pp. 227 - 239

We prove the existence of multiple positive solutions of the Dirichlet problem for the prescribed mean curvature equation in Minkowski space {−div(∇u/1−|∇u|2)=f(x,u,∇u)in Ω,u=0on ∂Ω. Here Ω...

Critical point theory | Multiplicity | Positive solution | Minkowski space | Non-existence | Quasilinear elliptic equation | Dirichlet boundary condition | Mean curvature | Topological degree | Existence | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Critical point theory | Multiplicity | Positive solution | Minkowski space | Non-existence | Quasilinear elliptic equation | Dirichlet boundary condition | Mean curvature | Topological degree | Existence | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Journal Article

Journal de mathématiques pures et appliquées, ISSN 0021-7824, 12/2016, Volume 106, Issue 6, pp. 1122 - 1140

We are interested in providing new results on the following prescribed mean curvature equation in Lorentz–Minkowski space∇⋅[∇u1−|∇u|2...

Quasilinear Elliptic Equations | ODEs techniques | Mean curvature operator | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Quasilinear Elliptic Equations | ODEs techniques | Mean curvature operator | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Journal Article

Advances in nonlinear analysis, ISSN 2191-9496, 06/2018, Volume 8, Issue 1, pp. 1227 - 1234

In this paper, we consider the analogous of the Hénon equation for the prescribed mean curvature problem in
, both in the Euclidean and in the Minkowski spaces...

ODEs techniques | Quasilinear elliptic equations | mean curvature operator | 35J62 | 35J93 | 35A24 | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | odes techniques | quasilinear elliptic equations | 35a24 | 35j93 | 35j62

ODEs techniques | Quasilinear elliptic equations | mean curvature operator | 35J62 | 35J93 | 35A24 | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | odes techniques | quasilinear elliptic equations | 35a24 | 35j93 | 35j62

Journal Article

Communications on pure and applied analysis, ISSN 1534-0392, 09/2012, Volume 11, Issue 5, pp. 1911 - 1922

...; by using the Second Fundamental Form we relate it to the Classical and Levi Mean Curvature...

Characteristic direction for hypersurfaces | Quasilinear degenerate elliptic PDEs | Viscosity solutions | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Characteristic direction for hypersurfaces | Quasilinear degenerate elliptic PDEs | Viscosity solutions | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Journal Article

Georgian mathematical journal, ISSN 1072-947X, 03/2017, Volume 24, Issue 1, pp. 113 - 134

We discuss existence, multiplicity, localisation and stability properties of solutions
of the Dirichlet problem associated with the gradient dependent prescribed mean curvature equation in the Lorentz...

quasilinear elliptic problem | multiplicity | 35J75 | 35J62 | 35J93 | 35B35 | existence | partial differential equation | 35J25 | orderinstability | Dirichlet condition | lower and upper solutions | 47H07 | Mean curvature | order stability | Lorentz–Minkowski space | order instability | Lorentz-Minkowski space | Physical Sciences | Mathematics | Science & Technology

quasilinear elliptic problem | multiplicity | 35J75 | 35J62 | 35J93 | 35B35 | existence | partial differential equation | 35J25 | orderinstability | Dirichlet condition | lower and upper solutions | 47H07 | Mean curvature | order stability | Lorentz–Minkowski space | order instability | Lorentz-Minkowski space | Physical Sciences | Mathematics | Science & Technology

Journal Article

7.
Full Text
Positive solutions for quasilinear elliptic inequalities and systems with nonlocal terms

Journal of Differential Equations, ISSN 0022-0396, 11/2019, Volume 268, Issue 10, pp. 6033 - 6066

... (which includes the m-Laplace and the m-mean curvature operator) we obtain optimal ranges of exponents p,q and α...

m-Laplace operator | Quasilinear elliptic inequalities | Existence and nonexistence of positive solutions | m-Mean curvature operator | Physical Sciences | Mathematics | Science & Technology

m-Laplace operator | Quasilinear elliptic inequalities | Existence and nonexistence of positive solutions | m-Mean curvature operator | Physical Sciences | Mathematics | Science & Technology

Journal Article

Journal of the Australian Mathematical Society (2001), ISSN 1446-7887, 08/2016, Volume 101, Issue 1, pp. 118 - 144

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 03/2017, Volume 262, Issue 6, pp. 3759 - 3804

..., ∞-Laplace, mean curvature of graph, and even strongly degenerate operators, in addition to some nonlocal quasilinear operators appearing in the existing literature...

Infinity-Laplace | Local limits | p-Laplace | Nonlocal quasilinear equations | Viscosity solutions | Well-posedness | Physical Sciences | Mathematics | Science & Technology | Analysis of PDEs

Infinity-Laplace | Local limits | p-Laplace | Nonlocal quasilinear equations | Viscosity solutions | Well-posedness | Physical Sciences | Mathematics | Science & Technology | Analysis of PDEs

Journal Article

10.
Full Text
On the Born–Infeld equation for electrostatic fields with a superposition of point charges

Annali di matematica pura ed applicata, ISSN 1618-1891, 10/2018, Volume 198, Issue 3, pp. 749 - 772

In this paper, we study the static Born–Infeld equation
$$\begin{aligned} -\mathrm {div}\left( \frac{\nabla u}{\sqrt{1-|\nabla u|^2}}\right) =\sum _{k=1}^n a_k...

Inhomogeneous quasilinear equation | Nonlinear electromagnetism | 35J62 | 35B65 | Mathematics, general | Mean curvature operator in the Lorentz–Minkowski space | Mathematics | 35B40 | Born–Infeld equation | 78A30 | 35Q60 | Physical Sciences | Mathematics, Applied | Science & Technology | Electric fields | Operators (mathematics) | Singularities | Asymptotic properties | Differential equations | Taylor series | Euler-Lagrange equation | Superposition (mathematics) | Mathematics - Analysis of PDEs

Inhomogeneous quasilinear equation | Nonlinear electromagnetism | 35J62 | 35B65 | Mathematics, general | Mean curvature operator in the Lorentz–Minkowski space | Mathematics | 35B40 | Born–Infeld equation | 78A30 | 35Q60 | Physical Sciences | Mathematics, Applied | Science & Technology | Electric fields | Operators (mathematics) | Singularities | Asymptotic properties | Differential equations | Taylor series | Euler-Lagrange equation | Superposition (mathematics) | Mathematics - Analysis of PDEs

Journal Article

Communications in contemporary mathematics, ISSN 0219-1997, 04/2017, Volume 19, Issue 2, p. 1650006

We provide sufficient conditions for the existence of a uniparametric family of entire spacelike graphs with prescribed mean curvature in a Friedmann–Lemaître–Robertson...

Singular f-Laplacian | Quasilinear elliptic equation | Dirichlet boundary condition | Prescribed mean curvature function | Friedmann-Lemâitre-Robertson-Walker spacetime | Entire spacelike graph | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Graphs | Dirichlet problem | Curvature

Singular f-Laplacian | Quasilinear elliptic equation | Dirichlet boundary condition | Prescribed mean curvature function | Friedmann-Lemâitre-Robertson-Walker spacetime | Entire spacelike graph | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Graphs | Dirichlet problem | Curvature

Journal Article

Monatshefte für Mathematik, ISSN 1436-5081, 11/2017, Volume 187, Issue 2, pp. 315 - 325

...Monatsh Math (2018) 187:315–325
https://doi.org/10.1007/s00605-017-1133-z
Positive solutions for Dirichlet problems involving
the mean curvature operator...

34B27 | 34B05 | 34B15 | Minkowski space | Mathematics, general | Quasilinear differential equation | Mathematics | Leray–Schauder fixed point theorem | 34A40 | Existence | Positive radial solution | Mean curvature operator | Physical Sciences | Science & Technology | Differential equations | Operators (mathematics) | Fixed points (mathematics) | Boundary value problems | Mathematical analysis | Dirichlet problem | Curvature | Schauder fixpoint theorem | Continuity (mathematics)

34B27 | 34B05 | 34B15 | Minkowski space | Mathematics, general | Quasilinear differential equation | Mathematics | Leray–Schauder fixed point theorem | 34A40 | Existence | Positive radial solution | Mean curvature operator | Physical Sciences | Science & Technology | Differential equations | Operators (mathematics) | Fixed points (mathematics) | Boundary value problems | Mathematical analysis | Dirichlet problem | Curvature | Schauder fixpoint theorem | Continuity (mathematics)

Journal Article

Topological methods in nonlinear analysis, ISSN 1230-3429, 09/2014, Volume 44, Issue 1, pp. 23 - 39

We study the existence and multiplicity of positive radial solutions of the Dirichlet problem for the Minkowski-curvature equation
{ -div...

Radial solution | Variational methods | Multiplicity | Positive solution | Quasilinear elliptic differential equation | Minkowski-curvature | Dirichlet boundary condition | Existence | Physical Sciences | Mathematics | Science & Technology

Radial solution | Variational methods | Multiplicity | Positive solution | Quasilinear elliptic differential equation | Minkowski-curvature | Dirichlet boundary condition | Existence | Physical Sciences | Mathematics | Science & Technology

Journal Article

Journal of Geometric Analysis, ISSN 1050-6926, 7/2012, Volume 22, Issue 3, pp. 780 - 799

We prove the existence and uniqueness of graphs with prescribed mean curvature function in a large class of Riemannian manifolds which comprises spaces endowed...

Abstract Harmonic Analysis | 53C42 | Quasilinear elliptic PDE | 53A10 | Conformal Killing graphs | Fourier Analysis | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Mathematics | Dynamical Systems and Ergodic Theory | Differential Geometry | Prescribed mean curvature | Physical Sciences | Science & Technology

Abstract Harmonic Analysis | 53C42 | Quasilinear elliptic PDE | 53A10 | Conformal Killing graphs | Fourier Analysis | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Mathematics | Dynamical Systems and Ergodic Theory | Differential Geometry | Prescribed mean curvature | Physical Sciences | Science & Technology

Journal Article

Nonlinear analysis, ISSN 0362-546X, 02/2013, Volume 78, Issue 1, pp. 62 - 78

.... The main model cases are given by the p-Laplacian operator as well as the mean curvature operator in nonparametric form...

Quasilinear elliptic systems | Liouville theorems | A priori estimates | Carnot groups | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Operators | Mathematical analysis | Coercive force | Inequalities | Constrictions | Nonlinearity | Mathematical models | Curvature | Mathematics - Analysis of PDEs

Quasilinear elliptic systems | Liouville theorems | A priori estimates | Carnot groups | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Operators | Mathematical analysis | Coercive force | Inequalities | Constrictions | Nonlinearity | Mathematical models | Curvature | Mathematics - Analysis of PDEs

Journal Article

Nonlinear analysis, ISSN 0362-546X, 2010, Volume 72, Issue 11, pp. 4188 - 4199

...
of least-energy solutions goes to a point on the boundary
∂
Ω
at a rate of
o
(
ε
)
and this point on the boundary approaches a global maximum point of mean curvature...

Least-energy solution | Quasilinear Neumann problem | Mean curvature [formula omitted]-Laplacian operator | Exponential decay | Mean curvature m-Laplacian operator | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Neumann problem | Positioning | Mathematical analysis | Boundary conditions | Nonlinearity | Complement | Boundaries | Curvature

Least-energy solution | Quasilinear Neumann problem | Mean curvature [formula omitted]-Laplacian operator | Exponential decay | Mean curvature m-Laplacian operator | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Neumann problem | Positioning | Mathematical analysis | Boundary conditions | Nonlinearity | Complement | Boundaries | Curvature

Journal Article

Bulletin of the Brazilian Mathematical Society, New Series, ISSN 1678-7544, 6/2018, Volume 49, Issue 2, pp. 279 - 312

We consider the quasilinear degenerate elliptic equation with rough and singular coefficients of the form $$\begin{aligned} div\left( {A(x,u,\nabla u)} \right...

35J60 | Theoretical, Mathematical and Computational Physics | Harnack’s inequality | 35J70 | Rough and singular coefficient | Mathematics, general | Mathematics | Quasilinear degenerate elliptic equation | Fefferman–Phong type inequality | Physical Sciences | Science & Technology | Equality | Elliptic functions | Coefficients | Quadratic forms | Smoothness | Continuity (mathematics) | Inequality

35J60 | Theoretical, Mathematical and Computational Physics | Harnack’s inequality | 35J70 | Rough and singular coefficient | Mathematics, general | Mathematics | Quasilinear degenerate elliptic equation | Fefferman–Phong type inequality | Physical Sciences | Science & Technology | Equality | Elliptic functions | Coefficients | Quadratic forms | Smoothness | Continuity (mathematics) | Inequality

Journal Article

Mathematical methods in the applied sciences, ISSN 0170-4214, 10/2020, Volume 43, Issue 15, pp. 8496 - 8505

...‐ and supersolution method to find solutions to problem (P). Further, we apply our result to some specific nonlocal prescribed mean curvature problems.

sub‐ and supersolution method | quasilinear operator | prescribed mean curvature equation | nonlocal problem | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Mathematical analysis | Curvature

sub‐ and supersolution method | quasilinear operator | prescribed mean curvature equation | nonlocal problem | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Mathematical analysis | Curvature

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 2011, Volume 250, Issue 2, pp. 675 - 689

... (submitted for publication)
[1], the latter in the context of mean curvature type operators, see Theorem 1.3 and Theorems 5.2–5.4 below.
Finally, Theorem...

Entire solutions | Liouville theorems | Quasilinear elliptic inequalities | Physical Sciences | Mathematics | Science & Technology

Entire solutions | Liouville theorems | Quasilinear elliptic inequalities | Physical Sciences | Mathematics | Science & Technology

Journal Article