On the Equivalence of Viscosity and Weak Solutions to Normalized and Parabolic Equations
- Artikkeli I: Siltakoski, Jarkko (2018). Equivalence of viscosity and weak solutions for the normalized p(x)-Laplacian. Calculus of Variations and Partial Differential Equations 57(4):Art. 95, 20,2018. DOI: 10.1007/s00526-018-1375-1
- Artikkeli II: Jarkko Siltakoski, Equivalence of viscosity and weak solutions for a p-parabolic equation. Preprint in arXiv
- Artikkeli III: Jarkko Siltakoski, Equivalence between radial solutions of different non-homogeneous p-Laplacian type equations. Preprint in arXiv
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Siltakoski, Jarkko (Springer, 2021)We study the relationship of viscosity and weak solutions to the equation partial derivative(t)u - Delta(p)u = f (Du), where p > 1 and f is an element of C(R-N) satisfies suitable assumptions. Our main result is that bounded ...
A systematic approach on the second order regularity of solutions to the general parabolic p-Laplace equation Feng, Yawen; Parviainen, Mikko; Sarsa, Saara (Springer, 2023)We study a general form of a degenerate or singular parabolic equation ut−|Du|γ(Δu+(p−2)ΔN∞u)=0 that generalizes both the standard parabolic p-Laplace equation and the normalized version that arises from stochastic game ...
Blanc, Pablo; Charro, Fernando; Manfredi, Juan J.; Rossi, Julio D. (Union Matematica Argentina, 2022)In this paper we characterize viscosity solutions to nonlinear parabolic equations (including parabolic Monge–Ampère equations) by asymptotic mean value formulas. Our asymptotic mean value formulas can be interpreted from ...
Ruosteenoja, Eero (University of Jyväskylä, 2017)
Siltakoski, Jarkko (Elsevier Inc., 2022)We prove the local gradient Hölder regularity of viscosity solutions to the inhomogeneous normalized p(x)-Laplace equation −Δp(x)Nu=f(x), where p is Lipschitz continuous, infp>1, and f is continuous and bounded.