Results 41 to 50 of about 420,318 (376)

Fundamental solutions for degenerate parabolic equations [PDF]

Acta Mathematica, 1974
This chapter explains the construction of a candidate for a fundamental solution and the existence, smoothness, and certain bounds for a fundamental solution Γ. The underlying assumptions were that ( a ij , ( x )) is uniformly positive definite and a ij , b i are bounded and uniformly Holder continuous. The chapter presents a proof of how if a ij ,
openaire   +3 more sources

Riesz potentials and nonlinear parabolic equations [PDF]

, 2013
The spatial gradient of solutions to nonlinear degenerate parabolic equations can be pointwise estimated by the caloric Riesz potential of the right hand side datum, exactly as in the case of the heat equation.
A. Cianchi, B.K. Driver, E. Acerbi, E. DiBenedetto, E. DiBenedetto, E.M. Stein, F. Duzaar, F. Duzaar, G. Mingione, G. Mingione, Giuseppe Mingione, J. Kinnunen, J. Kinnunen, J. Kinnunen, J. Kinnunen, L. Boccardo, L.I. Hedberg, M. Havin, N.C. Phuc, N.C. Phuc, N.S. Trudinger, P. Lindqvist, S. Campanato, T. Jin, T. Kilpeläinen, T. Kilpeläinen, T. Kuusi, T. Kuusi, T. Kuusi, T. Kuusi, T. Kuusi, Tuomo Kuusi   +31 more
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Asymptotic expansions for degenerate parabolic equations

Comptes Rendus. Mathématique, 2014
Abstract We prove asymptotic convergence results for some analytical expansions of solutions to degenerate PDEs with applications to financial mathematics. In particular, we combine short-time and global-in-space error estimates, previously obtained in the uniformly parabolic case, with some a priori bounds on “short cylinders”, and we achieve short ...
PASCUCCI, ANDREA, Stefano Pagliarani, PAGLIARANI, STEFANO   +2 more
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Degenerate singular parabolic problems with natural growth [PDF]

Opuscula Mathematica
In this paper, we study the existence and regularity results for nonlinear singular parabolic problems with a natural growth gradient term \[\begin{cases}\frac{\partial u}{\partial t}-\operatorname{div}((a(x,t)+u^{q})|\nabla u|^{p-2}\nabla u)+d(x,t)\frac{
Mounim El Ouardy, Youssef El Hadfi, Abdelaaziz Sbai   +2 more
doaj   +1 more source

Null controllability of one dimensional degenerate parabolic equations with first order terms [PDF]

Discrete & Continuous Dynamical Systems - B, 2019
In this paper we present a null controllability result for a degenerate semilinear parabolic equation with first order terms. The main result is obtained after the proof of a new Carleman inequality for a degenerate linear parabolic equation with first ...
J. Flores, L. Teresa
semanticscholar   +1 more source

Embedding Operators in Vector-Valued Weighted Besov Spaces and Applications

Journal of Function Spaces and Applications, 2012
The embedding theorems in weighted Besov-Lions type spaces 𝐵𝑙,𝑠𝑝,𝑞,𝛾 (Ω;𝐸0,𝐸) in which 𝐸0,𝐸 are two Banach spaces and 𝐸0⊂𝐸 are studied. The most regular class of interpolation space 𝐸𝛼 between 𝐸0 and E is found such that the mixed differential operator ...
Veli Shakhmurov
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Expansion of positivity to a class of doubly nonlinear parabolic equations

Electronic Journal of Qualitative Theory of Differential Equations, 2022
We establish the expansion of positivity of the nonnegative, local, weak solutions to the class of doubly nonlinear parabolic equations $$\partial_t (u^{q}) -\operatorname{div}{(|D u|^{p-2} D u)}=0, \qquad\ p>1 \ \text{and} \ q>0$$ considering ...
Eurica Henriques
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The regular free boundary in the thin obstacle problem for degenerate parabolic equations [PDF]

St. Petersburg Mathematical Journal, 2019
In this paper we study the existence, the optimal regularity of solutions, and the regularity of the free boundary near the so-called \emph{regular points} in a thin obstacle problem that arises as the local extension of the obstacle problem for the ...
Agnid Banerjee, D. Danielli, N. Garofalo, A. Petrosyan   +3 more
semanticscholar   +1 more source

On the Weak Characteristic Function Method for a Degenerate Parabolic Equation

Journal of Function Spaces, 2019
For a nonlinear degenerate parabolic equation, how to impose a suitable boundary value condition to ensure the well-posedness of weak solutions is a very important problem.
Huashui Zhan
doaj   +1 more source

Local Calderón-Zygmund estimates for parabolic equations in weighted Lebesgue spaces

Mathematics in Engineering, 2023
We prove local Calderón-Zygmund type estimates for the gradient of weak solutions to degenerate or singular parabolic equations of $ p $-Laplacian type with $ p > \frac{2n}{n+2} $ in weighted Lebesgue spaces $ L^q_w $.
Mikyoung Lee, Jihoon Ok
doaj   +1 more source