zbMATH — the first resource for mathematics

\(L^p\)-Abschätzungen und klassische Lösungen für nichtlineare Wellengleichungen. I. (German) Zbl 0318.35054

35L05 Wave equation
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
35L15 Initial value problems for second-order hyperbolic equations
42B05 Fourier series and coefficients in several variables
35B45 A priori estimates in context of PDEs
PDF BibTeX Cite
Full Text: DOI EuDML
[1] Brenner, P.: OnL p -L p? estimates for the wave-equation. Math. Z.145, 251-254 (1975) · Zbl 0321.35052
[2] Brenner, P., Thomée, V., Wahlbin, L. B.: Besov spaces and applications to difference methods for initial value problems. Lecture Notes in Mathematics Nr. 434, Springer Berlin-Heidelberg-New York 1975 · Zbl 0294.35002
[3] Browder, F. E.: On the spectral theory of elliptic differential operators I. Math. Ann.142, 22-130 (1961) · Zbl 0104.07502
[4] Calderón, A. P.: Lebesgue spaces of differentiable functions and distributions. In: Proceedings of Symposia in Pure Mathematics vol. IV, Partial Differential Equations (Berkeley 1960), pp. 33-49. Providence: American Mathematical Society 1961
[5] Heinz, E.: Über die Regularität der Lösungen nichtlinearer Wellengleichungen. Nachr. Akad. Wiss. Göttingen. II. math.-phys. Kl. Nr.2, 15-26 (1975) · Zbl 0303.35013
[6] Heinz, E., von Wahl, W.: Zu einem Satz von F. E. Browder über nichtlineare Wellengleichungen. Math. Z.141, 33-45 (1975) · Zbl 0289.35076
[7] Hörmander, L.: Estimates for translation-invariant operators onL p -spaces. Acta Math.104, 93-145 (1960) · Zbl 0093.11402
[8] Jörgens, K.: Das Anfangswertproblem in Großen für eine Klasse nichtlinearer Wellengleichungen. Math. Z.77, 295-308 (1961) · Zbl 0111.09105
[9] Littman, W.: Fourier transforms of surface carried measures and differentiability of surface averages. Bull. Amer. math. Soc.69, 766-770 (1963) · Zbl 0143.34701
[10] Pecher, H.: Die Existenz regulärer Lösungen für Cauchy-und Angfangs-Randwertprobleme nichtlinearer Wellengleichungen. Math. Z.140, 263-279 (1974) · Zbl 0287.35069
[11] Pecher, H.: Globale klassische Lösungen nichtlinearer Wellengleichungen für höhere Raumdimensionen. Nachr. Akad. Wiss. II. math.-phys. Kl. Nr.14, 221-232 (1975). · Zbl 0317.35058
[12] Strichartz, R. S.: Convolutions with kernels having singularities on a sphere. Trans. Amer. math. Soc.148, 461-471 (1970) · Zbl 0199.17502
[13] Strichartz, R. S.: A priori estimates for the wave equation and some applications. J. functional Analysis5, 218-235 (1970) · Zbl 0189.40701
[14] von Wahl, W.: Klassische Lösungen nichtlinearer Wellengleichungen im Großen. Math. Z.112, 241-279 (1969) · Zbl 0177.36602
[15] von Wahl, W.: Über nichtlineare Wellengleichungen mit zeitabhängigem elliptischen Hauptteil. Math. Z.142, 105-120 (1975) · Zbl 0299.35064
[16] von Wahl, W.: Regular solutions of initial-boundary value problems for linear and nonlinear wave equations I. Manuscripta math.13, 187-206 (1974) · Zbl 0289.35053
[17] von Wahl, W.: Regular solutions of initial-boundary value problems for linear and nonlinear wave equations II. Math. Z.142, 121-130 (1975) · Zbl 0301.35063
[18] von Wahl, W.:L p -decay rates for homogeneous wave-equations. Math. Z.120, 93-106 (1971) · Zbl 0212.44201
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.