Ir al contenido

Documat


The Holder continuity of the solutions to quasi-linear system of elliptic partial differential equations with singular coefficients

  • Yaremenko, Mykola I. [1]
    1. [1] National Technical University of Ukraine, ”Igor Sikorsky Kyiv Polytechnic Institute”.
  • Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 41, Nº. 1, 2022, págs. 197-216
  • Idioma: inglés
  • DOI: 10.22199/issn.0717-6279-4531
  • Enlaces
  • Resumen
    • This article establishes the Holder continuity of the solutions to a quasi-linear system of elliptic partial differential equations with singular coefficients under the assumption of its form-boundary.

  • Referencias bibliográficas
    • D. R. Adams and L. I. Hedberg. Function Spaces and Potential Theory. Berlin: Springer-Verlag, 1996.
    • S. Agmon, A. Douglis, and L. Nirenberg, “Estimates near the boundary for solutions of elliptic partial differential equations satisfying general...
    • A. G. Berlyiand and Yu. A. Semenov, “On the Lp-theory of Schrodinger semigroups”, Siberian mathematical journal, vol. 31, pp. 16-26, 1990.
    • H. Brezis and A. Pazy, “Semigroups of nonlinear contractions on convex sets”, Journal of functional analysis, vol. 6, no. 2, pp. 237–281,...
    • F. E. Browder, “Existence of periodic solutions for nonlinear equations of evolution”, Proceedings of the National Academy of sciences, vol....
    • F. E. Browder, “Nonlinear equations of evolution and nonlinear accretive operators in Banach spaces”, Bulletin of the American Mathematical...
    • M. G. Crandall and A. Pazy, “Semi-groups of nonlinear contractions and dissipative sets”, Journal of functional analysis, vol. 3, no. 3, pp....
    • J.-M. Bony, “Calcul symbolique et propagation des singularités pour les équations aux Dérivées partielles non linéaires”, Annales scientifiques...
    • H. Brezis, “Some variational problems with lack of compactness”, in Nonlinear functional analysis and its applications, F. Browder, Ed. Providence:...
    • H. Brezis and J. M. Coron, “Convergence of solutions of H-systems or how to blow bubbles”, Archive for rational mechanics and analysis, vol....
    • H. Brezis, J.-M. Coron, and E. H. Lieb, “Harmonic maps with defects”, Communications in mathematical physics, vol. 107, no. 4, pp. 649–705,...
    • H. Brezis and L. Nirenberg, “Positive solutions of nonlinear elliptic equations involving critical sobolev exponents”, Communications on pure...
    • F. Browder, “Fixed point theory and nonlinear problems”, Bulletin of the american mathematical society , vol. 9, pp. 1-39, 1983.
    • F. E. Browder and W. V. Petryshyn, “Approximation methods and the generalized topological degree for nonlinear mappings in Banach spaces”,...
    • L. Caffarelli, R. Kohn, and L. Nirenberg, “Partial regularity of suitable weak solutions of the navier-stokes equations”, Communications on...
    • L. Caffarelli, L. Nirenberg, and J. Spruck, “The Dirichlet problem for nonlinear second-order elliptic equations I. Monge-Ampégre equation”,...
    • M. G. Crandall and P.-L. Lions, “Viscosity solutions of Hamilton-Jacobi equations”, Transactions of the american mathematical society, vol....
    • B. Dacorogna, Weak Continuity and weak lower semi-continuity of nonlinear functionals, Berlin: Springer-Verlag, 1987.
    • E. B. Davies, One parameter semigroups, San Diego: Academic Press, 1980.
    • E. B. Davies, “Lp Spectral Theory of Higher-Order Elliptic Differential Operators”, Bulletin of the London mathematical society, vol. 29,...
    • E. DeGiorgi, “Sulla differenziabilita e l’analiticita delle estremali degli integrali multipli regolari”, Memorie della Reale accademia delle...
    • E. DeGiorgi, “Un esempio di estremali discontinue per un problema variazionale di tipo ellitico”, Bollettino della Unione Matematica Italiana....
    • R. J. DiPerna, “Compensated compactness and general systems of conservation laws”, Transactions of the American mathematical society, vol....
    • R. J. DiPerna and P. L. Lions, “On the cauchy problem for Boltzmann equations: Global existence and weak stability”, The annals of mathematics,...
    • R. J. DiPerna and A. Majda, “Reduced hausdorff dimension and concentration-cancellation for two-dimensional incompressible flow”, Journal...
    • L. C. Evans, Weak convergence methods for nonlinear partial differential equations. Providence: AMS, 1988.
    • L. Giacomelli and H. Knüpfer, “A free boundary problem of fourth order: Classical solutions in Weighted Hölder spaces”, Communications in...
    • M. Giaquinta, Multiple integrals in the calculus of variations and nonlinear elliptic systems, Princeton: Princeton University Press, 1983.
    • M. Giaquinta. Introduction to Regularity Theory for Nonlinear Elliptic Systems, Basel: Birkhauser, 1993.
    • B. Gidas, W.-M. Ni, and L. Nirenberg, “Symmetry and related properties via the maximum principle”, Communications in mathematical physics,...
    • D. Gilbarg and N. S. Trudinger, Elliptic partial differential equations of second order, 2nd ed., Berlin: Springer, 1983.
    • E. Giusti, Minimal Surfaces and Functions of Bounded Variation, Basel: Birkhauser, 1984.
    • R. Landes and V. Mustonen, “On pseudo-monotone operators and nonlinear noncoercive variational problems on unbounded domains”, Mathematische...
    • G. J. Minty, “Monotone (nonlinear) operators in Hilbert Space”, Duke mathematical journal, vol. 29, no. 3, pp. 341-346, 1962. https://doi.org/10.1215/s0012-7094-62-02933-2
    • G. J. Minty, “On the generalization of a direct method of the calculus of variations”, Bulletin of the American mathematical society, vol....
    • I. Miyadera, “On perturbation theory for semi-groups of operators”, Tohoku mathematical journal, vol. 18, no. 3, pp. 299-310, 1966.https://doi.org/10.2748/tmj/1178243419
    • J. Necas, Introduction to the theory of nonlinear elliptic equations, New York: Teubner and Wiley, 1983.
    • E. V. Radkevich, “Equations with nonnegative characteristic form. I”, Journal of mathematical sciences, vol. 158, no. 3, pp. 297–452, 2009....
    • E. Stein, Harmonic analysis: real variable methods, orthogonality, and oscillatory integrals, Princeton: Princeton University. Press, 1993.
    • M. Struwe, “A global compactness result for elliptic boundary value problems involving limiting nonlinearities”, Mathematische zeitschrift,...
    • J. Sylvester and G. Uhlmann, “A global uniqueness theorem for an inverse boundary value problem”, The annals of mathematics, vol. 125, no....
    • M. Taylor, Partial differential equations, 3 vols. Berlin: Springer, 1996.
    • L. Veron, Singularities of solutions of second order quasilinear equations, New York: Longman, 1996.
    • F. B. Weissler, “Single point blow-up for a semilinear initial value problem”, Journal of differential equations, vol. 55, no. 2, pp. 204–224,...
    • M. I. Yaremenko, “The existence of a solution of evolution and elliptic equations with singular coefficients”, Asian journal of mathematics...
    • M. I. Yaremenko, “Quasi-linear evolution and elliptic equations”, Journal of progressive research in mathematics, vol. 11, 13 pp. 1645-1669,...
    • M. I. Yaremenko, “The sequence of semigroups of nonlinear operators and their applications to study the Cauchy problem for parabolic equations”,...

Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno