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Behavior of Weak Solutions to the Boundary Value Problems for Second Order Elliptic Quasi-Linear Equation with Constant and Variable Nonlinearity Exponent in a Neighborhood of a Conical Boundary Point

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Numerical Analysis and Its Applications (NAA 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10187))

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Abstract

We study the behavior near the boundary conical point of weak solutions to the Dirichlet and Robin problems for elliptic quasi-linear second-order equation with the p-Laplacian and the strong nonlinearity in the right side, as well as we consider the Dirichlet problem for p(x)-harmonic functions. We establish the exact estimate of the solutions modulus for our problems near a conical boundary point of the type \(|u(x)|=O(|x|^{\varkappa })\).

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Author information

Authors and Affiliations

  1. A.G. and N.G. Stoletov Vladimir State University, Vladimir, Russia

    Yury Alkhutov

  2. University of Warmia and Mazury, Olsztyn, Poland

    Mikhail Borsuk & Sebastian Jankowski

Authors
  1. Yury Alkhutov
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  2. Mikhail Borsuk
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  3. Sebastian Jankowski
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Corresponding author

Correspondence to Mikhail Borsuk .

Editor information

Editors and Affiliations

  1. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Dimov

  2. Department of Applied Analysis, Eötvös Loránd University, Budapest, Hungary

    István Faragó

  3. Department of Applied Mathematics and Statistics, University of Rousse, Ruse, Bulgaria

    Lubin Vulkov

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Alkhutov, Y., Borsuk, M., Jankowski, S. (2017). Behavior of Weak Solutions to the Boundary Value Problems for Second Order Elliptic Quasi-Linear Equation with Constant and Variable Nonlinearity Exponent in a Neighborhood of a Conical Boundary Point. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Numerical Analysis and Its Applications. NAA 2016. Lecture Notes in Computer Science(), vol 10187. Springer, Cham. https://doi.org/10.1007/978-3-319-57099-0_1

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  • DOI: https://doi.org/10.1007/978-3-319-57099-0_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-57098-3

  • Online ISBN: 978-3-319-57099-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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