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Ein nichtlinearer Interpolationssatz und seine Anwendung auf nichtlineare Wellengleichungen. (German) Zbl 0384.35039


MSC:

35L05 Wave equation
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
47J05 Equations involving nonlinear operators (general)
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References:

[1] Bergh, J., Löfström, J.: Interpolation spaces. Berlin-Heidelberg-New York: Springer 1976 · Zbl 0344.46071
[2] Brenner P.: OnL p-Lp? estimates for the wave-equation. Math. Z.145, 251-254 (1975) · Zbl 0321.35052
[3] Calderón, A.P.: Lebesgue spaces of differentiable functions and distributions. In: Partial Differential Equations. Proceedings of a Symposion (Berkeley 1960), pp. 33-49. Proceedings of Symposia in Pure Mathematics vol. IV. Providence: American Mathematical Society 1961
[4] Heinz, E.: Über die Regularität der Lösungen nichtlinearer Wellengleichungen. Nachr. Akad. Wiss. Göttingen, II. math.-phys. Kl. Jahrgang 1975, Nr. 2, 15-26 · Zbl 0303.35013
[5] Pecher, H.:L p-Abschätzungen und klassische Lösungen für nichtlineare Wellengleichungen I. Math. Z.150, 159-183 (1976) · Zbl 0347.35053
[6] Pecher, H.:L p-Abschätzungen und klassische Lösungen für nichtlineare Wellengleichungen II. Manuscripta Math.20, 227-244 (1977) · Zbl 0359.35051
[7] Tartar, L.: Inteipolation non linéaire et regularité. J. Functional Analysis9, 469-489 (1972) · Zbl 0241.46035
[8] Triebel, H.: Spaces of distributions of Besov type on Euclideann-space. Duality, interpolation. Ark. Mat.11, 13-64 (1973) · Zbl 0255.46026
[9] von Wahl, W.: Klassische Lösungen nichtlinearer Wellengleichungen im Großen. Math. Z.112, 241-279 (1969) · Zbl 0177.36602
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