Erratum to the paper I.A. Ryzhkova "On Trace Regularity of Solutions to a Wave Equation with Homogeneous Neumann Boundary Conditions" (J.Math. Phys. Anal. Geom., 3 (2007), No. 4, 468-489)
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2011
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| Zitieren: | Erratum to the paper I.A. Ryzhkova "On Trace Regularity of Solutions to a Wave Equation with Homogeneous Neumann Boundary Conditions" (J.Math. Phys. Anal. Geom., 3 (2007), No. 4, 468-489) // Журнал математической физики, анализа, геометрии. — 2011. — Т. 7, № 2. — С. 193. — англ. |
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Journal of Mathematical Physics, Analysis, Geometry
2011, vol. 7, No. 2, pp. 193
Errata
Erratum to the paper I.A. Ryzhkova "On Trace Regularity of Solutions to a
Wave Equation with Homogeneous Neumann Boundary Conditions" (J.
Math. Phys. Anal. Geom., 3 (2007), No. 4, 468�489).
There are errors in the statements of Theorem 3 (ii), Corollary 1 (ii), Theo-
rem 4 (ii) of the paper. In these points the space L∞(0, T ;H−1/4+θ−ε(B)) and
the norm in it are to be replaced by the space L∞(0, T ;H−1/2+θ−ε(B)) and the
corresponding norm. Thus, these statements must look as follows.
Theorem 3. (ii): (∂t + U∂x1)γ[φ] = f1 + f2, where f1 ∈
L∞(0, T ;H−1/2+θ−ε
loc (R2)) for any ε > 0, f2 ∈ L2(0, T ;Hθ
loc(R2)), and
||f1||L∞(0,T ;H−1/2+θ−ε(B)) ≤ C(T, U,B, ε)
(
||∇φ0||θ,R3
+
+ ||φ1||θ,R3
+
)
,
||f2||L2(0,T ;Hθ(B)) ≤ C(T, U,B)
(
||∇φ0||θ,R3
+
+ ||φ1||θ,R3
+
)
for any bounded set B ⊂ R2.
Theorem 4. (ii): Let f ∈ L∞(R+; Hθ(R3
+)). Then (∂t +U∂x1)γ[φ] = f1 + f2,
where f1 ∈ L∞(0, T ; H−1/2+θ−ε(R2)), ε > 0, f2 ∈ L2(0, T ; Hθ(R2)), and the
following estimates are valid:
||f1||L∞(0,T ;H−1/2+θ−ε(R2)) ≤ C(T, U, ε)||f ||L∞(R+;Hθ(R3
+)),
||f2||L2(0,T ;Hθ(R2)) ≤ C(T, U)||f ||L∞(R+;Hθ(R3
+)).
Appropriate changes should be made in Corollary 1 (ii) and in the proofs of
these theorems. The statements of Theorem 3 (i), Corollary 1 (i), Theorem 4 (i)
hold true as formulated in the paper.
Journal of Mathematical Physics, Analysis, Geometry, 2011, vol. 7, No. 2 193
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irk-123456789-1066722020-11-17T17:05:07Z Erratum to the paper I.A. Ryzhkova "On Trace Regularity of Solutions to a Wave Equation with Homogeneous Neumann Boundary Conditions" (J.Math. Phys. Anal. Geom., 3 (2007), No. 4, 468-489) 2011 Article Erratum to the paper I.A. Ryzhkova "On Trace Regularity of Solutions to a Wave Equation with Homogeneous Neumann Boundary Conditions" (J.Math. Phys. Anal. Geom., 3 (2007), No. 4, 468-489) // Журнал математической физики, анализа, геометрии. — 2011. — Т. 7, № 2. — С. 193. — англ. 1812-9471 http://dspace.nbuv.gov.ua/handle/123456789/106672 en Журнал математической физики, анализа, геометрии Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| format |
Article |
| title |
Erratum to the paper I.A. Ryzhkova "On Trace Regularity of Solutions to a Wave Equation with Homogeneous Neumann Boundary Conditions" (J.Math. Phys. Anal. Geom., 3 (2007), No. 4, 468-489) |
| spellingShingle |
Erratum to the paper I.A. Ryzhkova "On Trace Regularity of Solutions to a Wave Equation with Homogeneous Neumann Boundary Conditions" (J.Math. Phys. Anal. Geom., 3 (2007), No. 4, 468-489) Журнал математической физики, анализа, геометрии |
| title_short |
Erratum to the paper I.A. Ryzhkova "On Trace Regularity of Solutions to a Wave Equation with Homogeneous Neumann Boundary Conditions" (J.Math. Phys. Anal. Geom., 3 (2007), No. 4, 468-489) |
| title_full |
Erratum to the paper I.A. Ryzhkova "On Trace Regularity of Solutions to a Wave Equation with Homogeneous Neumann Boundary Conditions" (J.Math. Phys. Anal. Geom., 3 (2007), No. 4, 468-489) |
| title_fullStr |
Erratum to the paper I.A. Ryzhkova "On Trace Regularity of Solutions to a Wave Equation with Homogeneous Neumann Boundary Conditions" (J.Math. Phys. Anal. Geom., 3 (2007), No. 4, 468-489) |
| title_full_unstemmed |
Erratum to the paper I.A. Ryzhkova "On Trace Regularity of Solutions to a Wave Equation with Homogeneous Neumann Boundary Conditions" (J.Math. Phys. Anal. Geom., 3 (2007), No. 4, 468-489) |
| title_sort |
erratum to the paper i.a. ryzhkova "on trace regularity of solutions to a wave equation with homogeneous neumann boundary conditions" (j.math. phys. anal. geom., 3 (2007), no. 4, 468-489) |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/106672 |
| citation_txt |
Erratum to the paper I.A. Ryzhkova "On Trace Regularity of Solutions to a Wave Equation with Homogeneous Neumann Boundary Conditions" (J.Math. Phys. Anal. Geom., 3 (2007), No. 4, 468-489) // Журнал математической физики, анализа, геометрии. — 2011. — Т. 7, № 2. — С. 193. — англ. |
| series |
Журнал математической физики, анализа, геометрии |
| first_indexed |
2025-07-07T18:50:44Z |
| last_indexed |
2025-07-07T18:50:44Z |
| _version_ |
1837015231873679360 |