# Trace Theorem and Applications

## Abstract

We characterize three-dimensional vector fields on the basis of the trace of a certain combination of normal derivatives, curl, and divergence. We clarify an unconditional connection between the values of a vector-valued function and the values of gradient, curl, and divergence on the boundary, which makes it possible to consider boundary value problems with boundary conditions that involve the basic first order differential operations of field theory.

- Authors:

- National Research University “Moscow Power Engineering Institute” (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22771582

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Sciences

- Additional Journal Information:
- Journal Volume: 228; Journal Issue: 6; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; BOUNDARY CONDITIONS; BOUNDARY-VALUE PROBLEMS; FIELD THEORIES; FUNCTIONS; THREE-DIMENSIONAL CALCULATIONS; VECTOR FIELDS

### Citation Formats

```
Dubinskii, Yu. A., E-mail: julii-dubinskii@mail.ru.
```*Trace Theorem and Applications*. United States: N. p., 2018.
Web. doi:10.1007/S10958-017-3653-4.

```
Dubinskii, Yu. A., E-mail: julii-dubinskii@mail.ru.
```*Trace Theorem and Applications*. United States. doi:10.1007/S10958-017-3653-4.

```
Dubinskii, Yu. A., E-mail: julii-dubinskii@mail.ru. Thu .
"Trace Theorem and Applications". United States. doi:10.1007/S10958-017-3653-4.
```

```
@article{osti_22771582,
```

title = {Trace Theorem and Applications},

author = {Dubinskii, Yu. A., E-mail: julii-dubinskii@mail.ru},

abstractNote = {We characterize three-dimensional vector fields on the basis of the trace of a certain combination of normal derivatives, curl, and divergence. We clarify an unconditional connection between the values of a vector-valued function and the values of gradient, curl, and divergence on the boundary, which makes it possible to consider boundary value problems with boundary conditions that involve the basic first order differential operations of field theory.},

doi = {10.1007/S10958-017-3653-4},

journal = {Journal of Mathematical Sciences},

issn = {1072-3374},

number = 6,

volume = 228,

place = {United States},

year = {2018},

month = {2}

}

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