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70 results on '"linear partial differential operator"'

4. MEAN VALUE THEOREMS FOR SOLUTIONS OF LINEAR PARTIAL DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS.

Author

Pokrovskii, Andrei V. and Trofymenko, Olga D.

Subjects
*MEAN value theorems, *PARTIAL differential equations, *EUCLIDEAN domains
Abstract

We prove a mean value theorem that characterizes continuous weak solutions of homogeneous linear partial differential equations with constant coefficients in Euclidean domains. In this theorem the mean value of a smooth function with respect to a complex Borel measure on an ellipsoid of special form is equal to some linear combination of its partial derivatives at the center of this ellipsoid. The main result of the paper generalizes a well-known Zalcman's theorem. [ABSTRACT FROM AUTHOR]

Published
2018
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7. Relations Between the Motion-Responses Caused by Fixed and Moving Loads Acting on Discretely Supported Strings and Beams

Author

Zoller, V., Zobory, I., Bock, Hans-Georg, editor, Dehoog, Frank, editor, Friedman, Avner, editor, Langford, William, editor, Neunzert, Helmut, editor, Pulleyblank, William R., editor, Rusten, Torgeir, editor, Tornberg, Anna-Karin, editor, Capasso, Vincenzo, editor, Mattheij, Robert, editor, Anile, Angelo Marcello, editor, and Greco, Antonio, editor

Published
2002
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9. On natural invariants and equivalence of differential operators.

Author

Lychagin, Valentin and Yumaguzhin, Valeriy

Subjects
*DIFFERENTIAL invariants, *NONLINEAR partial differential operators, *NONLINEAR operators, *PARTIAL differential operators
Abstract

We give a description of the field of rational natural differential invariants for a class of nonlinear differential operators of order k ≥ 2 on an n -dimensional manifold, n ≥ 2 , and apply the results to the equivalence problem of such operators. [ABSTRACT FROM AUTHOR]

Published
2023
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11. G

Author

Hazewinkel, Michiel and Hazewinkel, Michiel, editor

Published
2000
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16. Microlocal Analysis

Author

Wang, Rouhuai, Chen, Shuxing, Hazewinkel, M., editor, Gu, Chaohao, editor, Ding, Xiaxi, editor, and Yang, Chung-Chun, editor

Published
1994
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23. Some results on surjectivity of augmented differential operators

Author

Kalmes, T.

Subjects
*PARTIAL differential operators, *LINEAR operators, *FUNCTIONAL analysis, *MATHEMATICAL singularities, *CONVEX domains, *POLYNOMIALS, *MATHEMATICAL analysis, *PLANE geometry
Abstract

Abstract: Considering a problem of Bonet and Domański (2006) , we prove that for a polynomial P on surjectivity of the differential operator on implies surjectivity of the augmented operator on , where . Moreover we give a sufficient geometrical condition on an open subset X of such that an analogous implication is true for arbitrary dimension d in case of P being homogeneous, semi-elliptic, or of principal type. [Copyright &y& Elsevier]

Published
2012
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24. The splitting of exact sequences of PLS-spaces and smooth dependence of solutions of linear partial differential equations

Author

Bonet, José and Domański, Paweł

Subjects
*DIFFERENTIAL equations, *SCHWARTZ spaces, *PARTIAL differential operators, *VECTOR-valued measures
Abstract

Abstract: We investigate the splitting of short exact sequences of the form where E is the dual of a Fréchet Schwartz space and X, Y are PLS-spaces, like the spaces of distributions or real analytic functions or their subspaces. In particular, we characterize pairs as above such that in the category of PLS-spaces and apply this characterization to many natural spaces X and E. In particular, we discover an extension of the – splitting theorem of Vogt and Wagner. These abstract results are applied to parameter dependence of linear partial differential operators and surjectivity of such operators on spaces of vector-valued distributions. [Copyright &y& Elsevier]

Published
2008
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25. A hierarchy of generalized invariants for linear partial differential operators.

Author

Kartashova, E. A.

Subjects
*PARTIAL differential operators, *GAUGE invariance, *DIFFERENTIAL operators, *SYMMETRY (Physics), *MATHEMATICAL transformations
Abstract

We study invariants of linear partial differential operators in two variables under gauge transformations. Using the Beals-Kartashova factorization, we construct a hierarchy of generalized invariants for operators of an arbitrary order. We study the properties of these invariants and give some examples. We also show that the classic Laplace invariants correspond to some particular cases of generalized invariants. [ABSTRACT FROM AUTHOR]

Published
2006
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26. Parameter dependence of solutions of differential equations on spaces of distributions and the splitting of short exact sequences

Author

Bonet, José and Domański, Paweł

Subjects
*DIFFERENTIAL operators, *CONVEX sets, *SET theory, *MATHEMATICAL functions
Abstract

Abstract: We show that a linear partial differential operator with constant coefficients is surjective on the space of E-valued (ultra-)distributions over an arbitrary convex set if is a nuclear Fréchet space with property (DN). In particular, this holds if E is isomorphic to the space of tempered distributions or to the space of germs of holomorphic functions over a one-point set . This result has an interpretation in terms of solving the scalar equation such that the solution u depends on parameter whenever the right-hand side f also depends on the parameter in the same way. A suitable analogue for surjective convolution operators over is obtained as well. To get the above results we develop a splitting theory for short exact sequences of the formwhere Z is a Fréchet Schwartz space and X, Y are PLS-spaces, like the spaces of distributions or real analytic functions or their subspaces. In particular, an extension of the splitting theorem of Vogt and Wagner is obtained. [Copyright &y& Elsevier]

Published
2006
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43. Ill-Posed Problems

Author

Smoller, Joel, Artin, M., editor, Chern, S. S., editor, Doob, J. L., editor, Grothendieck, A., editor, Heinz, E., editor, Hirzebruch, F., editor, Hörmander, L., editor, Mac Lane, S., editor, Magnus, W., editor, Moore, C. C., editor, Moser, J. K., editor, Nagata, M., editor, Schmidt, W., editor, Scott, D. S., editor, Tits, J., editor, van der Waerden, B. L., editor, Berger, M., editor, Eckmann, B., editor, Varadhan, S. R. S., editor, and Smoller, Joel

Published
1983
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47. Interior regularity of solutions of differential equations

Author

Hörmander, Lars, Doob, J. L., editor, Heinz, E., editor, Hirzebruch, F., editor, Hopf, E., editor, Hopf, H., editor, Maak, W., editor, Magnus, W., editor, Schmidt, F. K., editor, Stein, K., editor, Eckmann, B., editor, van der Waerden, B. L., editor, and Hörmander, Lars

Published
1964
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48. Differential equations which have no solutions

Author

Hörmander, Lars, Doob, J. L., editor, Heinz, E., editor, Hirzebruch, F., editor, Hopf, E., editor, Hopf, H., editor, Maak, W., editor, MacLane, S., editor, Magnus, W., editor, Mumford, D., editor, Postnikov, M. M., editor, Schmidt, F. K., editor, Scott, D. S., editor, Stein, K., editor, Eckmann, B., editor, van der Waerden, B. L., editor, and Hörmander, Lars

Published
1969
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49. Some special spaces of distributions

Author

Hörmander, Lars, Doob, J. L., editor, Heinz, E., editor, Hirzebruch, F., editor, Hopf, E., editor, Hopf, H., editor, Maak, W., editor, MacLane, S., editor, Magnus, W., editor, Mumford, D., editor, Postnikov, M. M., editor, Schmidt, F. K., editor, Scott, D. S., editor, Stein, K., editor, Eckmann, B., editor, van der Waerden, B. L., editor, and Hörmander, Lars

Published
1969
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50. Differential equations which have no solutions

Author

Hörmander, Lars, Doob, J. L., editor, Grammel, R., editor, Heinz, E., editor, Hirzebruch, F., editor, Hopf, E., editor, Hopf, H., editor, Maak, W., editor, Magnus, W., editor, Schmidt, F. K., editor, Stein, K., editor, Eckmann, B., editor, Van Der Waerden, B. L., editor, and Hörmander, Lars

Published
1963
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