Sufficient Conditions for an Existence of a Solution to a Differential Inclusion

DOI: 10.68381/jca21038 ISSN: 0944-6532

Waldemar Pompe

We formulate geometric conditions induced by the compact set

K\subset\mathcal{R}^{m\times n}

K ⊂ R m × n

, which imply existence of a Lipschitz solution

u

to the differential inclusion

Du\in K

D u ∈ K

. The solutions are obtained using the convex integration method. We illustrate our result for the known example

K=SO(2)\cup SO(2)B

K = S O ( 2 ) ∪ S O ( 2 ) B

, where

B

is a

2\times2

2 × 2

diagonal matrix with

\det B=1

det ⁡ B = 1

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