A weighted Lq(Lp)-theory for fully degenerate second-order evolution equations with unbounded time-measurable coefficients

Ildoo Kim

doi:10.1007/s40072-024-00330-3

A weighted Lq(Lp)-theory for fully degenerate second-order evolution equations with unbounded time-measurable coefficients

Ildoo Kim^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We study the fully degenerate second-order evolution equation (Formula presented.) given with the zero initial data. Here a^ij(t), bⁱ(t), c(t) are merely locally integrable functions, and (aij(t))_d×d is a nonnegative symmetric matrix with the smallest eigenvalue δ(t)≥0. We show that there is a positive constant N such that (Formula presented.) where p,q∈(1,∞), α(t)=∫₀^tδ(s)ds, and w is Muckenhoupt’s weight.

Original language	English
Article number	107494
Pages (from-to)	80-106
Number of pages	27
Journal	Stochastics and Partial Differential Equations: Analysis and Computations
Volume	13
Issue number	1
DOIs	https://doi.org/10.1007/s40072-024-00330-3
Publication status	Published - 2025 Mar

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.

Keywords

Degenerate second-order parabolic equations
Weighted L-estimates
Zero initial-value problem

ASJC Scopus subject areas

Statistics and Probability
Modelling and Simulation
Applied Mathematics

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10.1007/s40072-024-00330-3

Cite this

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abstract = "We study the fully degenerate second-order evolution equation (Formula presented.) given with the zero initial data. Here aij(t), bi(t), c(t) are merely locally integrable functions, and (aij(t))d×d is a nonnegative symmetric matrix with the smallest eigenvalue δ(t)≥0. We show that there is a positive constant N such that (Formula presented.) where p,q∈(1,∞), α(t)=∫0tδ(s)ds, and w is Muckenhoupt{\textquoteright}s weight.",

keywords = "Degenerate second-order parabolic equations, Weighted L-estimates, Zero initial-value problem",

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note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.",

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N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.

PY - 2025/3

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N2 - We study the fully degenerate second-order evolution equation (Formula presented.) given with the zero initial data. Here aij(t), bi(t), c(t) are merely locally integrable functions, and (aij(t))d×d is a nonnegative symmetric matrix with the smallest eigenvalue δ(t)≥0. We show that there is a positive constant N such that (Formula presented.) where p,q∈(1,∞), α(t)=∫0tδ(s)ds, and w is Muckenhoupt’s weight.

AB - We study the fully degenerate second-order evolution equation (Formula presented.) given with the zero initial data. Here aij(t), bi(t), c(t) are merely locally integrable functions, and (aij(t))d×d is a nonnegative symmetric matrix with the smallest eigenvalue δ(t)≥0. We show that there is a positive constant N such that (Formula presented.) where p,q∈(1,∞), α(t)=∫0tδ(s)ds, and w is Muckenhoupt’s weight.

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KW - Weighted L-estimates

KW - Zero initial-value problem

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JO - Stochastics and Partial Differential Equations: Analysis and Computations

JF - Stochastics and Partial Differential Equations: Analysis and Computations

IS - 1

M1 - 107494

ER -

A weighted Lq(Lp)-theory for fully degenerate second-order evolution equations with unbounded time-measurable coefficients

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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