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References
Agmon, S., Lectures on Elliptic Boundary Value Problems. New York: Van Nostrand 1965.
Agmon, S., A. Douglis, & L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions I. Comm. Pure Appl. Math. 12, 623–727 (1959).
Barenblat, G., & G. Chernyi, On moment relations on surface discontinuity in dissipative media. J. Appl. Math. Mech. 27, 1205–1218 (1963).
Barenblat, G., I. Zhetov, & I. Kochina, Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks. J. Appl. Math. Mech. 24, 1286–1303 (1960).
Calderon, A. P., & A. Zygmund, On the existence of certain singular integrals. Acta Math. 88, 85–139 (1952).
Calderon, A. P., & A. Zygmund, On singular integrals. Amer. J. Math. 78, 289–309 (1956).
Carroll, R., Abstract Methods in Partial Differential Equations. New York: Harper and Row 1969.
Fichera, G., Linear Elliptic Differential Systems and Eigenvalue Problems, Lecture Notes, No. 8. New York: Springer 1965.
Fichera, G., Linear elliptic equations of higher order in two independent variables and singular integral equations with application to anisotropic inhomogeneous elasticity, Proceedings, Int. sym. P.D.E. and Cont. Mech., U. Wisc. Press, 1961.
Friedman, A., Generalized Functions and Partial Differential Equations. Englewood, N.J.: Prentice-Hall 1963.
Garabedian, P. R., Partial Differential Equations. New York: Wiley 1964.
Gelfand, I. M., & G. E. Shilov, Generalized Functions, Vols. 1,2. New York: Academic Press 1964, 1968.
Gilbert, R. P., Function Theoretic Methods in Partial Differential Equations. New York: Academic Press 1969.
Giraud, G., Généralisation des problèmes sur les opérations du type elliptique. Bull. Sci. Math. 56, 248–272, 281–312, 316–352 (1932).
Giraud, G., Sur quelques problèmes de Dirichlet et de Neumann. J. Math. Pures Appl. 11, 389–416 (1932).
Hörmander, L., Linear Partial Differential Operators. New York: Academic Press 1963.
Hörmander, L., Estimates for translation invariant operators. Acta Math. 104, 93–139 (1960).
Huilgol, R. R., A second order fluid of the differential type. Int. J. Non-linear Mech. 3, 471–482 (1968).
Lagnese, J. E., General boundary value problems for differential equations of Sobolev-Galpern type. Siam J. Math. Anal. 3, 273–284 (1972).
Mikhlin, S. G., Multidimensional Singular Integrals and Singular Integral Equations, English Edition. Oxford: Pergamon Press 1965.
Miranda, C., Sulle proprietà e la regolarità di certe transformazioni integrali. Mem. Acc. Lincei 7, 303–336 (1965).
Miranda, C., Partial Differential Equations of Elliptic Type. New York: Springer 1970.
Morrey, C. B., Second order elliptic equations in several variables and Hölder continuity. Math. Z. 72 (1959).
Moser, J., A new proof of De Giorgi's theorem concerning the regularity problem for elliptic differential equations. Comm. Pure Appl. Math. 13, 383–396 (1960).
Nash, J., Continuity of the solutions of parabolic and elliptic equations. Amer. J. Math. 80, 931–954 (1958).
Schwartz, L., Théorie des Distributions, Chap. VII. Paris: Hermann 1966.
Showalter, R. E., Partial differential equations of Sobolev-Galpern type. Pacific J. Math. 31, 789–794 (1969); Local regularity of solutions of partial differential equations of Sobolev-Galpern type. Ibid, 34, 781–787 (1970).
Showalter, R. E., Well-posed problems for a partial differential equation of order 2m+1. Siam J. Math. Anal. 1, 214–231 (1970).
Showalter, R. E., Weak solutions of non-linear evolution equations of Sobolev-Galpern type. J. Diff. Equations 11, 252–265 (1972).
Showalter, R. E., & T. W. Ting, Pseudo-parabolic partial differential equations. Siam J. Math. Anal. 1, 1–26 (1970).
Showalter, R. E., & T. W. Ting, Asymptotic behavior of solutions of pseudo-parabolic partial differential equations. Ann. Math. Pura. Appl. 90, 241–258 (1971).
Taylor, D. W., Research on Consolidation of Clays. Mass. Int. Tech. Press, Cambridge 1952.
Ting, T. W., Certain non-steady flows of second order fluids. Arch. Rational Mech. Anal. 14, 1–26 (1963).
Ting, T. W., Parabolic and pseudo-parabolic partial differential equations. J. Math. Soc. Japan 21, 440–453 (1969).
Yosida, K., Functional Analysis. New York: Academic Press 1965.
Zemanian, A. H., Distribution Theory and Transform Analysis. New York: McGraw-Hill 1965.
Zygmund, A., Trignometrical Series, I, II. London: Cambridge University Press 1959.
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Communicated by G. Fichera
This work was partially supported by National Science Foundation Grant GP-33174X.
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Gopala Rao, V.R., Ting, T.W. Solutions of pseudo-heat equations in the whole space. Arch. Rational Mech. Anal. 49, 57–78 (1972). https://doi.org/10.1007/BF00281474
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DOI: https://doi.org/10.1007/BF00281474