Nonlinear Analysis, ISSN 0362-546X, 03/2015, Volume 115, pp. 50 - 61

...” which allows the use of Campanato’s notion of near operators, an idea developed for the 2nd order case.

Compensated compactness | Baire category method | Elliptic first order systems | Fully nonlinear systems | Convex Integration | Cordes’ condition | Cauchy–Riemann equations | Calculus of variations | Campanato’s near operators | Campanato's near operators | Cordes' condition | Cauchy-Riemann equations | MATHEMATICS, APPLIED | NEARNESS | EQUATIONS | MATHEMATICS | OPERATORS | Operators | Fourier transforms | Perturbation methods | Partial differential equations | Uniqueness | Nonlinearity | Devices | Estimates

Compensated compactness | Baire category method | Elliptic first order systems | Fully nonlinear systems | Convex Integration | Cordes’ condition | Cauchy–Riemann equations | Calculus of variations | Campanato’s near operators | Campanato's near operators | Cordes' condition | Cauchy-Riemann equations | MATHEMATICS, APPLIED | NEARNESS | EQUATIONS | MATHEMATICS | OPERATORS | Operators | Fourier transforms | Perturbation methods | Partial differential equations | Uniqueness | Nonlinearity | Devices | Estimates

Journal Article

Nonlinear Differential Equations and Applications NoDEA, ISSN 1021-9722, 6/2016, Volume 23, Issue 3, pp. 1 - 30

We consider the problem of existence and uniqueness of strong a.e. solutions $${u: \mathbb{R}^n \longrightarrow \mathbb{R}^N}$$ u : R n ⟶ R N to the fully...

Cordes’condition | Primary 35J46 | 35J60 | Secondary 35D30 | Fully nonlinear systems | Elliptic 2nd order systems | Convex Integration | Mathematics | 35J47 | Calculus of Variations | 32W50 | Analysis | Baire Category method | 32A50 | Campanato’s near operators | SINGULAR SOLUTIONS | MATHEMATICS, APPLIED | NEARNESS | Campanato's near operators | SOLVABILITY | Cordes' condition | MINIMIZATION PROBLEMS | MAPS | DIRICHLET PROBLEM | EQUATION | OPERATORS

Cordes’condition | Primary 35J46 | 35J60 | Secondary 35D30 | Fully nonlinear systems | Elliptic 2nd order systems | Convex Integration | Mathematics | 35J47 | Calculus of Variations | 32W50 | Analysis | Baire Category method | 32A50 | Campanato’s near operators | SINGULAR SOLUTIONS | MATHEMATICS, APPLIED | NEARNESS | Campanato's near operators | SOLVABILITY | Cordes' condition | MINIMIZATION PROBLEMS | MAPS | DIRICHLET PROBLEM | EQUATION | OPERATORS

Journal Article

Advances in Nonlinear Analysis, ISSN 2191-9496, 05/2018, Volume 7, Issue 2, pp. 139 - 148

In the very recent paper [ ], the second author proved that for any , the fully nonlinear first order system is well posed in the so-called J. L. Lions space...

Baire category method | 35J60 | elliptic first order systems | Cauchy–Riemann equations | 35J47 | 35J46 | compensated compactness | convex integration | 32W50 | calculus of variations | Cordes’ condition | 35D30 | fully nonlinear systems | 32A50 | Campanato’s near operators | Campanato's near operators | Cordes' condition | Cauchy-Riemann equations | MATHEMATICS | MATHEMATICS, APPLIED

Baire category method | 35J60 | elliptic first order systems | Cauchy–Riemann equations | 35J47 | 35J46 | compensated compactness | convex integration | 32W50 | calculus of variations | Cordes’ condition | 35D30 | fully nonlinear systems | 32A50 | Campanato’s near operators | Campanato's near operators | Cordes' condition | Cauchy-Riemann equations | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

4.
Full Text
Generalised solutions for fully nonlinear PDE systems and existence–uniqueness theorems

Journal of Differential Equations, ISSN 0022-0396, 07/2017, Volume 263, Issue 1, pp. 641 - 686

We introduce a new theory of generalised solutions which applies to fully nonlinear PDE systems of any order and allows for merely measurable maps as...

Young measures | Generalised solutions | Baire Category method | Laplacian | Fully nonlinear systems | Campanato's near operators | SINGULAR SOLUTIONS | MATHEMATICS | MAPS | infinity-Laplacian | EQUATION | MINIMIZATION PROBLEMS

Young measures | Generalised solutions | Baire Category method | Laplacian | Fully nonlinear systems | Campanato's near operators | SINGULAR SOLUTIONS | MATHEMATICS | MAPS | infinity-Laplacian | EQUATION | MINIMIZATION PROBLEMS

Journal Article

Revista matemática complutense, ISSN 1988-2807, 2017, Volume 31, Issue 2, pp. 287 - 331

We consider the commutators [b, T] and $$[b,I_{\rho }]$$ [b,Iρ] , where T is a Calderón–Zygmund operator, $$I_{\rho }$$ Iρ is a generalized fractional integral...

Commutator | Campanato space | Mathematics | Variable growth condition | Topology | Morrey space | Geometry | 42B35 | Algebra | 42B25 | Analysis | Singular integral | 46E30 | 42B20 | Fractional integral | Mathematics, general | Applications of Mathematics

Commutator | Campanato space | Mathematics | Variable growth condition | Topology | Morrey space | Geometry | 42B35 | Algebra | 42B25 | Analysis | Singular integral | 46E30 | 42B20 | Fractional integral | Mathematics, general | Applications of Mathematics

Journal Article

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, ISSN 1021-9722, 05/2016, Volume 23, Issue 3

.... The proof is based on the solvability of the linearised problem by Fourier transform methods, together with a "perturbation device" which allows to use Campanato's near operators. We also discuss our hypothesis via counterexamples and give a stability theorem of strong global solutions for systems of the form (1).

SINGULAR SOLUTIONS | MATHEMATICS, APPLIED | NEARNESS | Fully nonlinear systems | Elliptic 2nd order systems | Campanato's near operators | Convex Integration | SOLVABILITY | Calculus of Variations | Cordes' condition | MINIMIZATION PROBLEMS | MAPS | Baire Category method | DIRICHLET PROBLEM | EQUATION | OPERATORS

SINGULAR SOLUTIONS | MATHEMATICS, APPLIED | NEARNESS | Fully nonlinear systems | Elliptic 2nd order systems | Campanato's near operators | Convex Integration | SOLVABILITY | Calculus of Variations | Cordes' condition | MINIMIZATION PROBLEMS | MAPS | Baire Category method | DIRICHLET PROBLEM | EQUATION | OPERATORS

Journal Article

7.
Full Text
Orthogonality in locally convex spaces: Two nonlinear generalizations of Neumann's lemma

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 04/2020, Volume 484, Issue 1, p. 123663

.... This work is related to the Birkhoff-James orthogonality and to the concept of near operators introduced by S. Campanato.

Campanato nearness | Söderlind-Campanato lemma | Neumann lemma | Birkhoff-Kakutani-Day-James theorem | Birkhoff-James orthogonality | Casazza-Christenses lemma | Soderlind-Campanato lemma | MATHEMATICS | MATHEMATICS, APPLIED | OPERATORS

Campanato nearness | Söderlind-Campanato lemma | Neumann lemma | Birkhoff-Kakutani-Day-James theorem | Birkhoff-James orthogonality | Casazza-Christenses lemma | Soderlind-Campanato lemma | MATHEMATICS | MATHEMATICS, APPLIED | OPERATORS

Journal Article

Mathematische Nachrichten, ISSN 1522-2616, 2019, Volume 292, Issue 6, pp. 1392 - 1407

Given a Lipschitz domain D⊂Rd, a Calderón–Zygmund operator T and a modulus of continuity ω(x...

truncated Calderón–Zygmund operators | Campanato spaces | 42B20 | T1 theorem | MATHEMATICS | HARDY-SPACES | truncated Calderon-Zygmund operators | SOBOLEV SPACES

truncated Calderón–Zygmund operators | Campanato spaces | 42B20 | T1 theorem | MATHEMATICS | HARDY-SPACES | truncated Calderon-Zygmund operators | SOBOLEV SPACES

Journal Article

Journal of function spaces, ISSN 2314-8896, 1/2014, Volume 2014, pp. 1 - 11

< ∞ , but not on L 1 . Using Orlicz spaces, we can investigate the boundedness of the maximal operator near p = 1 more precisely (see [6–8]). It is well known that the Riesz...

MATHEMATICS | MATHEMATICS, APPLIED | MAXIMAL FUNCTIONS | CAMPANATO SPACES | INEQUALITY | HARDY-SPACES | EQUATIONS | BOUNDEDNESS | INTEGRAL-OPERATORS | Function space | Commutators

MATHEMATICS | MATHEMATICS, APPLIED | MAXIMAL FUNCTIONS | CAMPANATO SPACES | INEQUALITY | HARDY-SPACES | EQUATIONS | BOUNDEDNESS | INTEGRAL-OPERATORS | Function space | Commutators

Journal Article

The Journal of geometric analysis, ISSN 1050-6926, 2012, Volume 24, Issue 2, pp. 1007 - 1051

... only on a class of admissible balls, and then obtain the boundedness of the local Hardy–Littlewood maximal operator and the local fractional integral operator on such Morrey-type spaces...

Campanato space | Riesz transform | Mathematics | Morrey space | Abstract Harmonic Analysis | 42B35 | Fourier Analysis | 42B25 | Convex and Discrete Geometry | Singular integral | 42B20 | Global Analysis and Analysis on Manifolds | Gauss measure space | Differential Geometry | Dynamical Systems and Ergodic Theory | Locally doubling measure space | EXTENSIONS | ORNSTEIN-UHLENBECK SEMIGROUP | BMO | MAXIMAL-FUNCTION | COMMUTATORS | POTENTIALS | H-1 | MATHEMATICS | METRIC MEASURE-SPACES | NON-DOUBLING MEASURES | OPERATORS

Campanato space | Riesz transform | Mathematics | Morrey space | Abstract Harmonic Analysis | 42B35 | Fourier Analysis | 42B25 | Convex and Discrete Geometry | Singular integral | 42B20 | Global Analysis and Analysis on Manifolds | Gauss measure space | Differential Geometry | Dynamical Systems and Ergodic Theory | Locally doubling measure space | EXTENSIONS | ORNSTEIN-UHLENBECK SEMIGROUP | BMO | MAXIMAL-FUNCTION | COMMUTATORS | POTENTIALS | H-1 | MATHEMATICS | METRIC MEASURE-SPACES | NON-DOUBLING MEASURES | OPERATORS

Journal Article

HOKKAIDO MATHEMATICAL JOURNAL, ISSN 0385-4035, 02/2019, Volume 48, Issue 1, pp. 99 - 140

.... If geometric behavior of the velocity vector field near the maximum point has a kind of stationary Euler flow configuration up to a possible blowup time, then the solution can be extended to be the strong solution beyond the possible blowup time. As another application we also mention the Cauchy problem for the Navier-Stokes equation.

BMO | blowup criterion | HARDY-SPACES | REGULARITY CRITERION | Cauchy problem | UNIQUENESS | 3D Navier-Stokes equation | MATHEMATICS | stationary 3D Euler flow | MORREY | POINTWISE MULTIPLIERS | Campanato spaces with variable growth condition | INTEGRAL-OPERATORS | WEAK SOLUTIONS

BMO | blowup criterion | HARDY-SPACES | REGULARITY CRITERION | Cauchy problem | UNIQUENESS | 3D Navier-Stokes equation | MATHEMATICS | stationary 3D Euler flow | MORREY | POINTWISE MULTIPLIERS | Campanato spaces with variable growth condition | INTEGRAL-OPERATORS | WEAK SOLUTIONS

Journal Article

Mathematische Annalen, ISSN 0025-5831, 11/2006, Volume 336, Issue 3, pp. 617 - 637

...Math. Ann. (2006) 336: 617–637 DOI 10.1007/s00208-006-0014-x Mathematische Annalen Applications of the differential calculus to nonlinear elliptic operators...

35J65 | 58C15 | 35R05 | DERIVATIVE PROBLEM | MATHEMATICS | VMO COEFFICIENTS | LINEAR EQUATIONS | SOBOLEV-CAMPANATO SPACES | BOUNDARY-VALUE-PROBLEMS | BMO COEFFICIENTS | NONSMOOTH DATA | MEAN OSCILLATION | DOMAINS

35J65 | 58C15 | 35R05 | DERIVATIVE PROBLEM | MATHEMATICS | VMO COEFFICIENTS | LINEAR EQUATIONS | SOBOLEV-CAMPANATO SPACES | BOUNDARY-VALUE-PROBLEMS | BMO COEFFICIENTS | NONSMOOTH DATA | MEAN OSCILLATION | DOMAINS

Journal Article

10/2000, ISBN 3527401350, 12

... 3.1.3 Near Operators in Hilbert Spaces

discontinuous coefficients | Hilbert spaces | nonlinear operators | Campanato's condition

discontinuous coefficients | Hilbert spaces | nonlinear operators | Campanato's condition

Book Chapter

Acta Applicandae Mathematicae, ISSN 0167-8019, 12/2015, Volume 140, Issue 1, pp. 1 - 9

We consider the regularity criterion for the three dimensional incompressible Navier-Stokes equations in terms of one directional derivative of the velocity....

Weak solution | Theoretical, Mathematical and Computational Physics | Mechanics | Morrey-Campanato space | 35B65 | Mathematics, general | Mathematics | 35Q30 | Computer Science, general | Statistical Physics, Dynamical Systems and Complexity | Regularity | Navier-Stokes equations | SPACE | MATHEMATICS, APPLIED | WEAK SOLUTIONS | Fluid dynamics | Studies | Theorems | Mathematical models | Navier Stokes equations | Applied mathematics | Velocity | Mathematical analysis | Texts | Derivatives | Criteria | Three dimensional

Weak solution | Theoretical, Mathematical and Computational Physics | Mechanics | Morrey-Campanato space | 35B65 | Mathematics, general | Mathematics | 35Q30 | Computer Science, general | Statistical Physics, Dynamical Systems and Complexity | Regularity | Navier-Stokes equations | SPACE | MATHEMATICS, APPLIED | WEAK SOLUTIONS | Fluid dynamics | Studies | Theorems | Mathematical models | Navier Stokes equations | Applied mathematics | Velocity | Mathematical analysis | Texts | Derivatives | Criteria | Three dimensional

Journal Article

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