# Quasielliptic Operators and Equations Not Solvable with Respect to the Higher Order Derivative

## Abstract

We consider a class of quasielliptic operators in R{sup n} and establish the isomorphism property in special weighted Sobolev spaces. In more general weighted spaces, we obtain the unique solvability conditions for quasielliptic equations and prove estimates for solutions. Based on the obtained results, we study the solvability of the initial problem for equations that are not solvable with respect to the higher order derivative.

- Authors:

- Sobolev Institute of Mathematics SB RAS (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22771408

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Sciences

- Additional Journal Information:
- Journal Volume: 230; Journal Issue: 1; 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; EQUATIONS; MATHEMATICAL OPERATORS; MATHEMATICAL SOLUTIONS; MATHEMATICAL SPACE

### Citation Formats

```
Demidenko, G. V., E-mail: demidenk@math.nsc.ru.
```*Quasielliptic Operators and Equations Not Solvable with Respect to the Higher Order Derivative*. United States: N. p., 2018.
Web. doi:10.1007/S10958-018-3723-2.

```
Demidenko, G. V., E-mail: demidenk@math.nsc.ru.
```*Quasielliptic Operators and Equations Not Solvable with Respect to the Higher Order Derivative*. United States. doi:10.1007/S10958-018-3723-2.

```
Demidenko, G. V., E-mail: demidenk@math.nsc.ru. Sun .
"Quasielliptic Operators and Equations Not Solvable with Respect to the Higher Order Derivative". United States. doi:10.1007/S10958-018-3723-2.
```

```
@article{osti_22771408,
```

title = {Quasielliptic Operators and Equations Not Solvable with Respect to the Higher Order Derivative},

author = {Demidenko, G. V., E-mail: demidenk@math.nsc.ru},

abstractNote = {We consider a class of quasielliptic operators in R{sup n} and establish the isomorphism property in special weighted Sobolev spaces. In more general weighted spaces, we obtain the unique solvability conditions for quasielliptic equations and prove estimates for solutions. Based on the obtained results, we study the solvability of the initial problem for equations that are not solvable with respect to the higher order derivative.},

doi = {10.1007/S10958-018-3723-2},

journal = {Journal of Mathematical Sciences},

issn = {1072-3374},

number = 1,

volume = 230,

place = {United States},

year = {2018},

month = {4}

}

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