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The Uniformly Parabolic Equations of Higher Order with Discontinuous Data in Generalized Morrey Spaces and Elliptic Equations in Unbounded Domains

<p id="p1">We study the regularity of the solutions of the Cauchy-Dirichlet problem for linear uniformly parabolic equations of higher order with vanishing mean oscillation (VMO) coefficients. We prove continuity in generalized parabolic Morrey spaces <span class="inline-formula"><mml:math xmlns:mml...

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Autores principales: Gadjiev, Tair, Suleymanova, Konul
Formato: Capítulo de libro
Lenguaje:inglés
Publicado: IntechOpen 2021
Materias:
Physical Sciences, Engineering and Technology
Acceso en línea:https://www.intechopen.com/chapters/75864
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Sumario:<p id="p1">We study the regularity of the solutions of the Cauchy-Dirichlet problem for linear uniformly parabolic equations of higher order with vanishing mean oscillation (VMO) coefficients. We prove continuity in generalized parabolic Morrey spaces <span class="inline-formula"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m1"><mml:msub><mml:mi>M</mml:mi><mml:mrow><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mi>&phi;</mml:mi></mml:mrow></mml:msub></mml:math></span> of sublinear operators generated by the parabolic Calderon-Zygmund operator and by the commutator of this operator with bounded mean oscillation (BMO) functions. We obtain strong solution belongs to the generalized Sobolev-Morrey space <span class="inline-formula"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m2"><mml:mover><mml:msubsup><mml:mi>W</mml:mi><mml:mrow><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mi>&phi;</mml:mi></mml:mrow><mml:mrow><mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mrow><mml:mo>&#8728;</mml:mo><mml:mspace width="0.8000001em"></mml:mspace></mml:mrow></mml:mover><mml:mfenced open="(" close=")"><mml:mi>Q</mml:mi></mml:mfenced></mml:math></span>. Also we consider elliptic equation in unbounded domains.</p>
ISBN:978-1-83968-656-6
DOI:10.5772/intechopen.96781

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