A note on the local regularity of distributional solutions and\n subsolutions of semilinear elliptic systems

2015/09/05 by Rainer Mandel, Mandel, Rainer
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1509.01731

openalex publication_date 2015/09/05 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

In this note we prove local regularity results for distributional solutions\nand subsolutions of semilinear elliptic systems such as L_k^m u_k =\nf_k(x,u₁,
ldots,u_N)
quad
textin
mathbbRⁿ
qquad (k=1,
ldots,N) where\nL₁,\…,L_N are of divergence-form and n\≥ 2m. We show that\ndistributional subsolutions are locally bounded from above if |f_k(x,z)|\≤\nC(1+|z|^p) for 1\≤ p<\(n)/(n-2m),k=1,\…,N.\n Furthermore, regularity properties of subsolutions and improved versions for\nbounded subsolutions are given. Even for f₁=\…=f_N=0 our results are\nnew.\n

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